Rohana J. Karunamuni's research while affiliated with University of Alberta and other places
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Publications (69)
Robust procedures in high-dimensional regression are important because outliers are often present in data. For data with heavy-tailed errors, quantile regression and least absolute deviation regression methods have been widely used with great success. Some interesting Huber-loss-based and robust M-type regularized estimators have also been develope...
In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimat...
Suppose that there are two populations which are mixed in proportions λ and (1-λ), respectively, and an investigator wishes to classify an individual into one of these two populations based on a p-dimensional observation on the individual. This is the basic classification problem with applications in wide variety of fields. In practice, the optimal...
Hematoma and edema volume are potential predictors of 30‐day mortality rate and functional outcome (degree of disability or dependence in daily activities after a stroke) for patients with intracerebral hemorrhage. The manual segmentation of hematoma and edema from computed tomography scans is common practice but a time‐consuming and labor‐intensiv...
We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robust...
In this paper, we investigate a hypothesis testing problem in regular semiparametric models using the Hellinger distance approach. Specifically, given a sample from a semiparametric family of \(\nu \)-densities of the form \(\{f_{\theta ,\eta }:\theta \in \Theta ,\eta \in \Gamma \},\) we consider the problem of testing a null hypothesis \(H_{0}:\th...
This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is suitable for more complicated data structures. However, its estimation inherits the difficulties and complexitie...
Finite mixture regression (FMR) models are frequently used in statistical modeling, often with many covariates with low significance. Variable selection techniques can be employed to identify the covariates with little influence on the response. The problem of variable selection in FMR models is studied here. Penalized likelihood-based approaches a...
Standard kernel density and regression estimators are well-known to be computationally very slow when analyzing large data sets, and algorithms that achieve considerable computational savings are highly desirable. With this goal in mind, two fast and accurate computational methods are proposed in this paper for computation of univariate and multiva...
In dose-response studies, experimenters are often interested in estimating the effective dose , the dose at which the probability of response is . For instance, in pharmacology studies one is typically interested in estimating , whereas in toxicology studies the main interest is for smaller values of . In this context, methods based on parametric,...
The successful application of the Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance (MHD) estimators, are efficient and have excellent robustness properties [Beran R. Minimum Hellinger distance estimators for parametric models. Ann Statist. 1977;5:445-463]...
Finite mixture models provide a mathematical basis for the statistical modeling of a wide variety of random situations, and their importance for the statistical analysis of data is well documented. This article focuses on a finite mixture regression model and develops an estimator of the parameters in the model using a minimum-distance technique. I...
Zhang et al. (2008) proposed a general minimum lower order confounding (GMC for short) criterion, which aims to select optimal factorial designs in a more elaborate and explicit manner. By extending the GMC criterion to the case of blocked designs, Wei et al. (submitted for publication) proposed a B1-GMC criterion. The present paper gives a constru...
Minimum distance techniques have become increasingly important tools for solving statistical estimation and inference problems. In particular, the successful application of the Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance estimators, achieve efficienc...
It is well known now that the minimum Hellinger distance estimation approach introduced by Beran (Beran, R., 1977. Minimum Hellinger distance estimators for parametric models. Ann. Statist. 5, 445–463) produces estimators that achieve efficiency at the model density and simultaneously have excellent robustness properties. However, computational dif...
We investigate the estimation problem of parameters in a two-sample semiparametric model. Specifically, let X1,...,Xn be a sample from a population with distribution function G and density function g. Independent of the Xi's, let Z1,...,Zm be another random sample with distribution function H and density function h(x)=exp[[alpha]+r(x)[beta]]g(x), w...
In this paper, we study the empirical Bayes two-action problem under linear loss function. Upper bounds on the regret of empirical Bayes testing rules are investigated. Previous results on this problem construct empirical Bayes tests using kernel type estimators of nonparametric functionals. Further, they have assumed specific forms, such as the co...
The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Stati...
Efficiency and robustness are two fundamental concepts in parametric estimation problems. It was long thought that there was an inherent contradiction between the aims of achieving robustness and efficiency; that is, a robust estimator could not be efficient and vice versa. It is now known that the minimum Hellinger distance approached introduced b...
This paper considers the nonparametric deconvolution problem when the true density function is left (or right) truncated. We propose to remove the boundary effect of the conventional deconvolution density estimator by using a special class of kernels: the deconvolution boundary kernels. Methods for constructing such kernels are provided. The mean s...
In this paper, we investigate the estimation problem of the mixture proportion λ in a nonparametric mixture model of the form λF(x)+(1-λ)G(x) using the minimum Hellinger distance approach, where F and G are two unknown distributions. We assume that data from the distributions F and G as well as from the mixture distribution λF+(1-λ)G are available....
The Receiver Operating Characteristic (ROC) curve is a statistical tool for evaluating the accuracy of diagnostics tests. The empirical ROC curve (which is a step function) is the most commonly used non-parametric estimator for the ROC curve. On the other hand, kernel smoothing methods have been used to obtain smooth ROC curves. The preceding proce...
Let X1,., Xn, be i.i.d. random variables with distribution function F, and let Y1,.,.,Yn be i.i.d. with distribution function G. For i = 1, 2,.,., n set δi, = 1 if Xi ≤ Yi, and 0 otherwise, and Xi, = min{Xi, Ki}. A kernel-type density estimate of f, the density function of F w.r.t. Lebesgue measure on the Borel o-field, based on the censored data (...
In this paper, the concept of asymptotic pointwise optimality in a single sequence of random variables provided by Bickel and Yahav [Bickel, P.J., Yahav, J.A., 1967. Asymptotically pointwise optimal procedures in sequential analysis. In: Proc Fifth Berkeley Symp. Math Statist. Prob. 1. University of California Press, pp. 401-413] is extended to mor...
In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this p...
In this paper, we investigate the empirical Bayes (EB) linear loss two-action problem for discrete distributions. Rates of convergence of the excess risk (the regret) of the EB rules are the main interest here. Previous results on the same problem have examined EB rules in the discrete exponential family or in particular types of discrete distribut...
Vendor evaluation is an important step for a manufacturer's purchasing operation. For firms adopting Just-In-Time Purchasing (JITP) strategy, vendor evaluation is critical in quality improvement and cost reduction. In this paper, we examine the value of information sharing in improving vendor evaluation. We build stochastic models for three differe...
Kernel smoothing methods are widely used in many research areas in statistics. However, kernel estimators suffer from boundary effects when the support of the function to be estimated has finite endpoints. Boundary effects seriously affect the overall performance of the estimator. In this article, we propose a new method of boundary correction for...
We investigate the empirical Bayes estimation problem of
multivariate regression coefficients under squared error loss
function. In particular, we consider the regression model
Y=Xβ+ε, where Y is an m-vector of observations, X is a known m×k matrix, β is an unknown k-vector, and ε is an m-vector of unobservable random variables. The problem is squa...
Kernel smoothing methods are widely used in many areas of statistics with great success. In particular, minimum distance procedures heavily depend on kernel density estimators. It has been argued that when estimating mixture parameters in finite mixture models, adaptive kernel density estimators are preferable over nonadaptive kernel density estima...
Choice of an appropriate kernel density estimator is a difficult one in minimum distance estimation based on density functions. Particularly, for mixture models, the choice of bandwidth is very crucial because the component densities may have different scale parameters, which in turn necessitate varying amount of smoothing. Adaptive kernel density...
The kernel method of estimation of curves is now popular and widely used in statistical applications. Kernel estimators suffer from boundary effects, however, when the support of the function to be estimated has finite endpoints. Several solutions to this problem have already been proposed. Here the authors develop a new method of boundary correcti...
It is well known now that kernel density estimators are not consistent when estimating a density near the finite end points of the support of the density to be estimated. This is due to boundary effects that occur in nonparametric curve estimation problems. A number of proposals have been made in the kernel density estimation context with some succ...
The well-known problem of multivariate calibration involves making inferences about an unknown q×1 vector X from a single random observed p×1 response vector Y. The relationship between Y and X is calibrated with experimental data (Xi,Yi), i=1,2,…,n, where Yi and Xi are p×1 and q×1 vectors, respectively, and satisfy the regression relationship Yi=α...
In this paper we adopt the dynamic system design approach to develop an integrated model system for the scrap-processing problem
under JIT and implement it as a kind of DSS plug-in for the ERP system. This solution represents the value-added migration
strategy toward the evolving global e-manufacturing operation. The convenience and flexibility of...
In this paper we study the empirical Bayes linear-loss two-action problem for the continuous one-parameter exponential family when the observed data are contaminated (errors in variables). A new empirical Bayes testing rule is constructed, and its asymptotic optimality uniformly over a class of prior distributions is established. Uniform rates of c...
In this article we investigate the estimation problem of the population mean of a finite population. Both point and interval estimators are of interest from Bayes and empirical Bayes point of views. Empirical Bayes analysis is concerned with the ‘current’ population mean, say γm, when the sample data are available from other similar (m−1) finite po...
We propose a new estimator for boundary correction for kernel density estimation. Our method is based on local Bayes techniques of Hjort (Bayesian Statist. 5 (1996) 223). The resulting estimator is semiparametric type estimator: a weighted average of an initial guess and the ordinary reflection method estimator. The proposed estimator is seen to pe...
In this article we investigate empirical Bayes procedures for estimates of binomial probabilities. We propose a sequential approach (vs. the usual fixed sample size) for esti mation of p. The small sample behaviour of the proposed method is studied through a Monte Carlo experiment based on dataset applications drawn from carcinogenesis bioassays. M...
Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments ac...
This paper considers empirical Bayes (EB) squared error loss estimation (SELE) in the location family. That is, the component problem is the SELE of <$>\theta<$> based on an observation Y having conditional (on <$>\theta<$>) density of the form <$>f_{0}(y - \theta)<$> for some known density function <$>f_{0}<$>. An EB estimator is constructed based...
Let (Y1,θ1),…,(Yn,θn) be independent real-valued random vectors with Yi, given θi, is distributed according to a distribution depending only on θi for i=1,…,n. In this paper, best linear unbiased predictors (BLUPs) of the θi's are investigated. We show that BLUPs of θi's do not exist in certain situations. Furthermore, we present a general empirica...
In this paper we consider the deconvolution problem in nonparametric density estimation. That is, one wishes to estimate the unknown density of a random variable X, say f
X
, based on the observed variables Y's, where Y = X + ∈ with ∈ being the error. Previous results on this problem have considered the estimation of f
X
at interior points. Here we...
Boundary effects are well known to occur in nonparametric density estimation when the support of the density has a finite endpoint. The usual kernel density estimators require modifications when estimating the density near endpoints of the support. In this paper, we propose a new and intuitive method of removing boundary effects in density estimati...
We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outpe...
Wc cansider the problem of a consnmer desiring to buy an item at as low a price as possible, based on a finite sequence of price quotations obtained sequentially. In this paper, we assume that the price search is concerned with minimizing the cumulative costs from the search.We investigate the situation in which the buyer must update the price dist...
In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f(0) is rather formidable due to boundary effects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modifications when estimating the density near endpoint...
Suppose that the random variable X is distributed according to exponential families of distributions, conditional on the parameter [theta]. Assume that the parameter [theta] has a (prior) distribution G. Because of the measurement error, we can only observe Y = X + [var epsilon], where the measurement error [theta] is independent of X and has a kno...
summaryThis paper proposes and investigates Fourier series estimators for length biased data. Specifically, two Fourier series estimators are constructed and studied based on ideas of Jones (1991) and Bhattacharyya et al. (1988) in the case of kernel density estimation. Approximate expressions for mean squared errors and integrated mean squared err...
This paper extends empirical Bayes estimators with the squared error loss for the continuous one-parameter exponential family when the observed data are contaminated. It is shown that the proposed empirical Bayes estimator is asymptotically optimal uniformly over a class of prior distributions. Furthermore, uniform rates of convergence of the corre...
The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how...
The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22–46, 247–264 and 402–413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes s...
We consider the empirical Bayes decision problem where the component problem is the sequential estimation of the mean ? of one-parameter exponential family of distributions with squared error loss for the estimation error and a cost c>0 for each observation. The present paper studies the untruncated sequential component case. In particular, an untr...
This paper develops a Bayesian model for estimating the density of a closed animal population from data obtained by the line transect method. The detection function is assumed to be half-normal and the data are neither grouped nor truncated. A Bayes estimator is constructed with respect to a gamma prior density and two loss functions: relative squa...
Empirical Bayes tests for testing Ho: 0 < 0 against H1: θ > 0 for the continu- ous one-parameter exponential family are considered. The loss function is piecewise linear. The monotonocity of the problem can be used to obtain both Bayes and empirical Bayes monotone rules for the problem. A Van Houwelingen (1976) - type monotone empirical Bayes test...
We consider the problem of a consumer desiring to buy an item at as low a price as possible based on a finite sequence of price quotations obtained sequentially from various sellers. This is a version of the so-called best-choice problem. It is assumed that the optimal decision is concerned with the probability-maximizing approach. When the distrib...
In this paper,the performance of asymptotically pointwise optimal procedures is studied for fixed c, the cost per unit sample. Our treatment is focused on a statistical hypothesis testing problem, namely,the linear loss two-action problem. Using the empirical Bayes approach, we construct a sequential testing procedure which dominates the A.P.O. tes...
We consider the empirical Bayes problem where the component problem is the sequential estimation of the mean of a distribution with squared error decision loss plus a sampling cost. An empirical Bayes sequential estimation procedure is exhibited which is asymptotically optimal. Asymptotic efficiency of the empirical Bayes stopping time sequence is...
Let X1,…,Xn denote a random sample from an unknown univariate distribution with density f. In kernel density estimation, one usually assumes that the density f belongs to some class , in order to obtain rate of convergence results. The various investigations in the literature differ in the classes of functions employed, these varying according to s...
Let X
1, X
2, ..., X
n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0d...
Some known kernel type estimates of a density and its derivatives f(p) are considered. Strong uniform consistency properties over the whole real line are studied. Improved rate of convergence results are established under substantially weaker smoothness assumptions of f(p), p [greater-or-equal, slanted] 0. A new bias reduction technique is presente...
The empirical Bayes approach to multiple decision problems with a sequential decision problem as the component is studied. An empirical Bayesm-truncated sequential decision procedure is exhibited for general multiple decision problems. With a sequential component, an empirical Bayes sequential decision procedure selects both a stopping rule functio...
We consider the empirical Bayes linear loss two-action problem in exponential families, λβ(λ)u(x), determined by a measure with Lebesgue density u, where u>0 if and only if x>a, and the parameter λ has a distribution G. Based on a sequence of observations X1,X2.. ,Xn, i.i.d. according to the marginal distribution of x, estimates of the posterior me...
We study the empirical Bayes approach to the sequential estimation problem. An empirical Bayes sequential decision procedure, which consists of a stopping rule and a terminal decision rule, is constructed for use in the component. Asymptotic behaviors of the empirical Bayes risk and the empirical Bayes stopping times are investigated as the number...
We study the empirical Bayes decision theory with an $m$-truncated sequential statistical decision problem as the component. An empirical Bayes sequential decision procedure is constructed for the linear loss two-action problem. Asymptotic results are presented regarding the convergence of the Bayes risk of the empirical Bayes sequential decision p...
P. Laippala [Scand. J. Stat., Theory Appl. 6, 113-118 (1979; Zbl 0456.62030); correction ibid. 7, 105 (1980); and Ann. Inst. Stat. Math. 37, 315-327 (1985; Zbl 0583.62008)] has defined a concept within the empirical Bayes framework that he calls “floating optimal sample size”. We examine this concept and show that it is one of many possibilities re...
Citations
... Finally, we extended the Wilcoxon-type regression in the framework of multivariate regression. However, several robust reduced-rank regressions for multivariate regression have also been proposed [Chao et al., 2021, Ding et al., 2021, Wang and Karunamuni, 2022, Tan et al., 2022, Mishra and Müller, 2022, Zhao et al., 2017, She and Chen, 2017 to deal with correlation of the response variables. The difference between our proposed method and these robust reduced-rank methods is that the proposed method has a clustering term to group the fitted values of the response variables, which allows the correlation among the response variables to be considered. ...
... (0↑900) β ∈ (0.5, 1] 900 2808.1 900 statistical methods. For more references on statistical methods, see, e.g., [35][36][37]. We hope that these important open problems can be addressed in the future research. ...
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... The skull removal step is proposed to extract the soft brain tissue and narrow down the region of interest. As the skull region usually has a higher intensity, a simple skull removal technique can be applied using thresholding (Tu et al., 2019), (Shahangian & Pourghassem, 2016). In (Farzaneh et al., 2017), (Yao et al., 2019), the seed for soft brain tissue was initialized by thresholding and then the soft tissue was segmented using the distance regularized level set evolution (DRLSE) method. ...
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... Specifically, the nonzero mean-shift parameter estimates were identified as outliers and an L 1 penalty was imposed on the regression parameters to facilitate the selection of important predictors. Karunamuni et al. (2019) proposed a new penalized procedure that simultaneously attains full efficiency and maximum robustness by imposing adaptive weights on both the decision loss and penalty function. Furthermore, the optimal convergence rate of L 1 -penalized Huber's M-estimator under the mean-shift model was studied by Dalalyan and Thompson (2019). ...
... The literature is too extensive for a complete listing here. Some recent developments and important references can be found in the articles Wu and Karunamuni [50][51][52] and Tang and Karunamuni [45,46], and in the monograph of Basu et al. [2]. ...
... MMSE score is one of the most widely-used tests of cognitive functions such as orientation, attention, memory, language and visual-spatial skills for assessing dementia severity.A more detailed description of the data can be found at http://adni.loni.usc.edu. Previous studies, such as Li, Huang, and Zhu (2017) and Tang et al. (2021), focused on building regression models to investigate the relationship between AD status progression and neuroimaging and demographic data. However, our main objective is to use DTI data and demographic and genetic features to predict AD status. ...
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... Several algorithms have been proposed to solve the LASSO problem. Among the most notable examples, the LARS algorithm [8]; greedy approaches, as the coordinate descent method [10]; robust distance-based techniques [25]. ...
... Recently, there is a growing interest in empirical Bayes procedures based on variables contaminated with errors. Zhang and Karunamuni [14], [15] and Pensky [6] have studied empirical Bayes estimation problem with errors in variables. Karunamuni and Zhang [3] have investigated empirical Bayes testing procedures for the continuous one-parameter exponential family with errors in variables. ...
... There have been numerous papers in the literature setting out various EB tests with different upper bounds on the corresponding regrets in terms of rates of convergence under variety of conditions on the prior G and on the family of distributions {F : ∈ }. The literature is too extensive to warrant a complete listing here; see, e.g., Johns and Van Ryzin (1972), Van Houwelingen (1976), Stijnen (1982Stijnen ( , 1985, Karunamuni (1996Karunamuni ( , 1999, Karunamuni and Yang (1995), Karunamuni and Zhang (2003), Pensky (2003), Liang (2000Liang ( , 2004Liang ( , 2006, Li and Gupta (2001, 2002, 2005 and Wang (2006) among others. In all of above papers and in many others which are not listed here, the particular EB rules that have been studied are mainly based on kernel type estimators of nonparametric functionals. ...
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... Primary and secondary variables are assumed to be sampled from a multivariate distribution that is unknown and must be inferred from available samples. Various techniques are available for multivariate distribution modeling such as kernel density estimation (Tong and Karunamuni 2016;Jones 1989), radial basis function networks (Bishop 1995), fitting copula functions (Boardman and Vann 2011; Reddy and Singh 2014), the stepwise conditional transform (Leuangthong and Deutsch 2003;Rosenblatt 1952) and the projection pursuit multivariate transformation or PPMT (Barnett et al. 2014). There are numerous methods in existence because none of them can handle all possible multivariate features that have been encountered with sample data collected from natural phenomena or from other sources. ...
