Abhik Ghosh

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Verified

Abhik verified their affiliation via an institutional email.

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• PhD
• Professor (Associate) at Indian Statistical Institute

Technical Report - Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, 2013: The power divergence (PD) and the density power divergence (DPD) families have proved to be useful tools in the area of robust inference. The families have striking similarities, but also have fundamental differences; yet both families are extremel...

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most of the applications consider the objective priors and need critical investigations (Efron, 2013, Science). And although it has several optimal properties, one major drawback of Bayesian inference is the lack of robustness a...

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression are based on $\ell_1$-penalization, and their theoretical properties are not well-investigated. In contrast,...

Applied sciences, including longitudinal and clustered studies in biomedicine, require analyses of ultrahigh-dimensional linear mixed effects models, where we need to select important fixed-effect variables from a large pool of available candidates. However, prior studies assume that all available covariates and random-effect components are indepen...

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization of the entropy and the minimization of the cross entropy or relative entropy (divergence), are essential for g...

This study explores the citation diversity in scholarly literature, analyzing different patterns of citations observed within different countries and academic disciplines. We examine citation distributions across top institutions within certain countries and find that the higher end of the distribution follows a Power Law or Pareto Law pattern; the...

The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the prese...

This manuscript delves into the intersection of genomics and phenotypic prediction, focusing on the statistical innovation required to navigate the complexities introduced by noisy covariates and confounders. The primary emphasis is on the development of advanced robust statistical models tailored for genomic prediction from single nucleotide polym...

In various practical situations, we encounter data from stochastic processes which can be efficiently modeled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, maximum likelihood (ML) estimation, the most common approach, is sensitive to slight model deviations or data contamination due to its well-known lack of...

In recent years, we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a moderately high dimension will now become computationally infeasible or unstable. Hence, there is a need for a pre...

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite common. Robust PCA methods using M-estimators have theoretical benefits, but their robustness drop substantially fo...

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model misspecification and the presence of outliers in the data; on the other hand robust estimators with reasonably hi...

Despite linear regression being the most popular statistical modelling technique, in real-life we often need to deal with situations where the true relationship between the response and the covariates is nonlinear in parameters. In such cases one needs to adopt appropriate non-linear regression (NLR) analysis, having wider applications in biochemic...

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination. In particul...

This study explores global citation diversity,examining its various patterns across countries and academic disciplines.We analyzed citation distributions in top institutes worldwide,revealing that the higher citation end of the distribution follow Power law or Pareto law pattern and the Pareto law's scaling exponent changes with the number of insti...

In real life, we frequently encounter ordinal variables depending upon independent covariates. The latent linear regression model is useful for modelling such data. One can find the model's parameters' maximum likelihood estimate (MLE). Though noted for its optimum properties, a small proportion of outliers may destabilize the MLE. This paper uses...

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood loss function are sensitive to data contamination and other noise and, hence...

Statistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is necessary. The rainfall amount during a rainy month or a whole rainy season can take any positive value and som...

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regressio...

Circular data are extremely important in many different contexts of natural and social science, from forestry to sociology, among many others. Since the usual inference procedures based on the maximum likelihood principle are known to be extremely non-robust in the presence of possible data contamination, in this paper, we develop robust estimators...

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination (e.g., video surveillanc...

In recent years we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a moderately high dimension will now become computationally infeasible. Hence, there is a need for a pre-screening of...

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to classical techniques based on maximum likelihood and related methods. Basu et al. (1998) introduced the density power divergence (DPD) family as a measure of discrepancy between two probability density functions and used this family for ro...

Arsenic (As) is a worldwide concern because of its toxic effects on crop yield and prevalence in the food chain. Rice is consumed by half of the world’s population and is known to accumulate As. The present study reviews the available literatures on As accumulation in different subspecies of rice grains (indica, japonica and aromatic) and performs...

Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measur...

In order to evaluate the impact of a policy intervention on a group of units over time, it is important to correctly estimate the average treatment effect (ATE) measure. Due to lack of robustness of the existing procedures of estimating ATE from panel data, in this paper, we introduce a robust estimator of the ATE and the subsequent inference proce...

We consider the problem of estimating diversity measures for a stratified population and discuss a general formulation for the entropy based diversity measures which includes the previously used entropies as well as a newly proposed family of logarithmic norm entropy (LNE) measures. Our main focus in this work is the consideration of statistical pr...

We consider the problem of variable screening in ultra‐high dimensional generalized linear models (GLMs) of non‐polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the margina...

Coronavirus disease 2019 (COVID19) has triggered a global pandemic affecting millions of people. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing the COVID-19 disease is hypothesized to gain entry into humans via the airway epithelium, where it initiates a host response. The expression levels of genes at the upper airway that in...

Urban scaling analysis in generally performed based on cities. In this study, we have (empirically) explored a new prospect for urban scaling analysis based on relatively larger local administrative units, which are independently functional, within a country. For this purpose, we have studied the scaling laws across Indian districts for the various...

In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is linearly related to the covariate(s), and takes a particular (ordinal) label depending on whether this latent vari...

In this brief note, we present the exponential consistency of the M-estimators of regression coefficients for models with multivariate responses. We first prove a exponential tail bound for the $\ell_2$-norm of the M-estimator from the true value of the regression coefficients under suitable assumption, which directly leads to the exponential consi...

Arsenic (As) is a worldwide concern because of its toxic effects on crop yield and prevalence in the food chain. Rice is consumed by half of the world’s population and is known to accumulate As. The present study reviews the available literatures on As accumulation in different subspecies of rice grains (indica, japonica and aromatic) and performs...

Robust estimation under multivariate normal (MVN) mixture model is always a computational challenge. A recently proposed maximum pseudo \b{eta}-likelihood estimator aims to estimate the unknown parameters of a MVN mixture model in the spirit of minimum density power divergence (DPD) methodology but with a relatively simpler and tractable computatio...

In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference methods based on the maximum likelihood (ML) principle are susceptible to minor deviations from assumed model o...

The estimation of extreme quantiles is one of the main objectives of statistics of extremes ( which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regressi...

Annotation of cells in single-cell clustering requires a homogeneous grouping of cell populations. Since single-cell data are susceptible to technical noise, the quality of genes selected prior to clustering is of crucial importance in the preliminary steps of downstream analysis. Therefore, interest in robust gene selection has gained considerable...

In order to evaluate the impact of a policy intervention on a group of units over time, it is important to correctly estimate the average treatment effect (ATE) measure. Due to lack of robustness of the existing procedures of estimating ATE from panel data, in this paper, we introduce a robust estimator of the ATE and the subsequent inference proce...

This paper reports a comprehensive study of distributional uncertainty in a few socio-economic indicators across the various states of India over the years 2001–2011. We show that the discrete generalized beta (DGB) distribution, a typical rank order distribution, provide excellent fits to the district-wise empirical data for the population size, l...

Hypothesis testing is one of the fundamental paradigms of statistical inference. The three canonical hypothesis testing procedures available in the statistical literature are the likelihood ratio (LR) test, the Wald test and the Rao (score) test. All of them have good optimality properties and past research has not identified any of these three pro...

A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach which classifies the tampered frames, and performs subsequent analysis on the remaining frames after discarding the tampered one...

Penalized logistic regression is extremely useful for binary classification with a large number of covariates (significantly higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood based loss function are sensitive to data contamination and...

Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre-screening of the variables may be necessary. A number of procedures for such pre-screening has been developed; among them the Sure Independence Screening (SIS) e...

In this paper, we introduce a robust estimator of the tail index of a Pareto-type distribution. The estimator is obtained through the use of the minimum density power divergence with an exponential regression model for log-spacings of top order statistics. The proposed estimator is compared to existing minimum density power divergence estimators of...

Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which generalizes the QDA and the minimum Mahalanobis distance (MMD) classifiers to discriminate between populations w...

We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from a first-order stationary Markov ch...

Annotation of cells in single-cell clustering requires a homogeneous grouping of cell populations. Since single cell data is susceptible to technical noise, the quality of genes selected prior to clustering is of crucial importance in the preliminary steps of downstream analysis. Therefore, interest in robust gene selection has gained considerable...

Systematic delineation of complex biological systems is an ever-challenging and resource-intensive process. Single cell transcriptomics allows us to study cell-to-cell variability in complex tissues at an unprecedented resolution. Accurate modeling of gene expression plays a critical role in the statistical determination of tissue-specific gene exp...

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering both skewed and symmetric cases. Since outliers are not uncommon in complex real-life experimental datasets, a ro...

This paper reports a comprehensive study of distributional uncertainty in a few socio-economic indicators across the various states of India over the years 2001-2011. We show that the DGB distribution, a typical rank order distribution, provide excellent fits to the district-wise empirical data for the population size, literacy rate (LR) and work p...

In this paper, we formulate a maximum entropy framework for a two-parameter Rank-Order (RO) distribution, namely the discrete generalized beta distribution (DGBD), which has recently been observed to be extremely useful in modeling several rank-size distributions from different context in Arts and Sciences, as a two-parameter generalization of Zipf...

With increasing availability of high dimensional, multi-source data, the identification of joint and data specific patterns of variability has become a subject of interest in many research areas. Several matrix decomposition methods have been formulated for this purpose, for example JIVE (Joint and Individual Variation Explained), and its angle bas...

This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical il...

Non‐parametric two‐sample problems are extremely important for applications in different applied disciplines. We define a general MI based on the φ divergences and use its estimate to propose a new general class of nonparametric two sample tests for continuous distributions. We derive the asymptotic distribution of the estimates of φ ‐divergence ba...

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is...

Many real-life data sets can be analyzed using Linear Mixed Models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measur...

Many single-cell typing methods require pure clustering of cells, which is susceptible towards the technical noise, and heavily dependent on high quality informative genes selected in the preliminary steps of downstream analysis. Techniques for gene selection in single-cell RNA sequencing (scRNA-seq) data are seemingly simple which casts problems w...

Feature selection is a key step in many machine learning tasks. A majority of the existing methods of feature selection address the problem by devising some scoring function while treating the features independently, thereby overlooking their interdependencies. We leverage the scale invariance property of copula to construct a greedy, supervised fe...

The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the prese...

As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). We propose a robust alternative to the ordinary likelihood approach for this estimation problem which performs simultaneous esti...

Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against data contamination. Some authors have overcome the problem of non-robustness by considering suitable loss functio...

We consider the problem of variable screening in ultra-high dimensional (of non-polynomial order) generalized linear models (GLMs). Since the popular SIS approach is extremely unstable in the presence of contamination and noises, which may frequently arise in the large scale sample data (e.g., Omics data), we discuss a new robust screening procedur...

Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A number of procedures for such pre-screening has been developed; among them the sure independence screening (SIS) e...

In this paper, we introduce a robust estimator of the tail index of a Pareto-type distribution. The estimator is obtained through the use of the minimum density power divergence with an exponential regression model for log-spacings of top order statistics. The proposed estimator is compared to existing minimum density power divergence estimators of...

We consider the problem of simultaneous model selection and the estimation of regression coefficients in high-dimensional linear regression models of non-polynomial order, an extremely important problem of the recent era. The adaptive penalty functions are used in this regard to achieve the oracle model selection property along with easier computat...

Quadratic discriminant analysis (QDA) is a widely used statistical tool to classify observations from different multivariate Normal populations. The generalized quadratic discriminant analysis (GQDA) classification rule/classifier, which generalizes the QDA and the minimum Mahalanobis distance (MMD) classifiers to discriminate between populations w...

We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via the minimization of a suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from the underlying first-order sta...

The ordinary Bayes estimator based on the posterior density suffers from the potential problems of non-robustness under data contamination or outliers. In this paper, we consider the general set-up of independent but non-homogeneous (INH) observations and study a robustified pseudo-posterior based estimation for such parametric INH models. In parti...

Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semiparametric Cox model is widely used to study different types of data arising from applied disciplines such as medical science, biology, and reliability studies. A fully parametric version o...

In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several rank-size distributions from different context in Arts and Sciences, as a two-parameter generalization of Zipf's law...

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering both skewed and symmetric cases. However, the existing likelihood based inference, that is routinely performed in...

Statistical modeling of rainfall is an important challenge in meteorology, particularly from the perspective of rainfed agriculture where a proper assessment of the future availability of rainwater is necessary. The probability models mostly used for this purpose are exponential, gamma, Weibull and lognormal distributions, where the unknown model p...

Statistical modeling of rainfall is an important challenge in meteorology , particularly from the perspective of rainfed agriculture where a proper assessment of the future availability of rainwater is necessary. The probability models mostly used for this purpose are exponential, gamma, Weibull and lognormal distributions, where the unknown model...

This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical il...

We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional guessing problem in the presence of some related side information, and the unconditional one where no such side...

Recently, applied sciences, including longitudinal and clustered studies in biomedicine require the analysis of ultra-high dimensional linear mixed effects models where we need to select important fixed effect variables from a vast pool of available candidates. However, all existing literature assume that all the available covariates and random eff...

We consider a two-parameter discrete generalized beta (DGB) distribution and propose its universal applications to study the size-distribution of the urban agglomerations across various countries in the world, where the urban agglomerations include the small and mid-sized cities along with the heavily populated cities. Our proposition is validated...

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is...

Entropy and cross-entropy are two very fundamental concepts in information theory and statistical physics and are also widely used for statistical inference across disciplines. In this paper, we will discuss a two parameter generalization of the popular Renyi entropy and associated optimization problems. We will derive the desired entropic characte...

We consider a class of density power divergence based tests for composite hypotheses under non-homogeneous data. This note provides a rigorous derivation of the power and level influence functions to theoretically justify their robustness with applications to fixed-carrier linear regressions.

Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semi-parametric Cox model is widely used to study different types of data arising from applied disciplines like medical science, biology, reliability studies and many more. A fully parametric v...

Robust tests of general composite hypothesis under non-identically distributed observations is always a challenge. Ghosh and Basu (2018, Statistica Sinica, 28, 1133--1155) have proposed a new class of test statistics for such problems based on the density power divergence, but their robustness with respect to the size and power are not studied in d...

We propose a universal two-parameter Rank-Ordering (RO) distribution for the urban agglomerations of various countries in the world, where the urban agglomerations include the small and mid-sized cities along with the heavily populated cities. Our proposition is validated by an exhaustive study with the data for India and China in 3 decades' census...

This paper describes a family of divergences, named herein as the C-divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics...

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robus...

Entropy and relative entropy measures play a crucial role in mathematical information theory. The relative entropies are also widely used in statistics under the name of divergence measures which link these two fields of science through the minimum divergence principle. Divergence measures are popular among statisticians as many of the correspondin...

We consider the problem of robust inference under the important generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and used this estimator to propose a robust Wald-type test for testing any general composite null hypothesis...

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the G...

This paper develops a new family of estimators, MDPDEs, as a robust generalization of maximum likelihood estimator for the polytomous logistic regression model (PLRM) by using the DPD measure. Based on these estimators, the family of Wald-type test statistics for linear hypotheses is introduced and their robust properties are theoretically studied...

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression are based on $\ell_1$-penalization, and their theoretical properties are not well-investigated. In contrast,...