Stanislav Volgushev

Cornell University | CU · Department of Statistical Science

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data‐driven methodology for learning the graphical structure. We show t...

Consider a panel data setting where repeated observations on individuals are available. Often it is reasonable to assume that there exist groups of individuals that share similar effects of observed characteristics, but the grouping is typically unknown in advance. We propose a novel approach to estimate such unobserved groupings for general panel...

Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions and thus avoiding the limitations of classical, $L^2$-based spectral methods. Most of...

In extreme value theory, the extremal variogram is a summary of the tail dependence of a random vector. It is a central ingredient for learning extremal tree structures (arXiv:2012.06179) and has close connections to the estimation of H\"usler-Reiss models and extremal graphical models (arXiv:1812.01734). This note presents concentration results fo...

Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from di...

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data-driven methodology for learning the graphical structure. We show t...

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing e...

We develop methodology for testing relevant hypotheses about functional time series in a tuning‐free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two‐sample problem this means that an L2‐distance betwe...

Nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data. In a large class of such models (including probit, proportional hazard and quantile regression to name just a few) it is impossible to difference out the individual effects, and inference is usually justified in a ‘large...

Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice however, block sizes are finite and observations from dif...

This article considers change point testing and estimation for high dimensional data. In the case of testing for a mean shift, we propose a new test which is based on U-statistics and utilizes the self-normalization principle. Our test targets dense alternatives in the high dimensional setting and involves no tuning parameters. The weak convergence...

Second order conditions provide a natural framework for establishing asymptotic results about estimators for tail related quantities. Such conditions are typically tailored to the estimation principle at hand, and may be vastly different for estimators based on the block maxima (BM) method or the peak-over-threshold (POT) approach. In this paper we...

In this paper we develop methodology for testing relevant hypotheses in a tuning-free way. Our main focus is on functional time series, but extensions to other settings are also discussed. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time series, we propose to test a relevant deviati...

Second order conditions provide a natural framework for establishing asymptotic results about estimators for tail related quantities. Such conditions are typically tailored to the estimation principle at hand, and may be vastly different for estimators based on the block maxima (BM) method or the peak-over-threshold (POT) approach. In this paper we...

Nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data. In a large class of such models (including probit, proportional hazard and quantile regression to name just a few) it is impossible to difference out individual effects, and inference is usually justified in a `large n l...

Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of time series models, but their applicability is seriously impacted by the limitations of covariances as a measu...

Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of time series models, but their applicability is seriously impacted by the limitations of covariances as a measu...

This paper introduces estimation methods for grouped latent heterogeneity in panel data quantile regression. We assume that the observed individuals come from a heterogeneous population with a finite number of types. The number of types and group membership is not assumed to be known in advance and is estimated by means of a convex optimization pro...

The uniqueness of the time-varying copula-based spectrum recently proposed by the authors is established via an asymptotic representation result involving Wigner–Ville spectra.

Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are replaced by alternative dependence measures which can be estimated by U-statistics. An interesting example is gi...

Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are replaced by alternative dependence measures which can be estimated by U-statistics. An interesting example is gi...

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop asymptotic theory for estimators of dependence measures or copula densities, they allow to derive tests for stochasti...

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parall...

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parall...

This paper investigates the problem whether the difference between two parametric models m1, m2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypothe...

The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.

The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.

In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular an asymptotic expansion and weak convergence to a Gaussian process are proved. The results can, on the one ha...

In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular an asymptotic expansion and weak convergence to a Gaussian process are proved. The results can, on the one ha...

This study analyzes the relation between works councils and overtime hours in Germany. The estimated effects differ considerably in dependence of standard contracted working time. Furthermore, we find differences across the quantiles of the overtime hours distribution and these differences between quantiles also vary between employees of establishm...

A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In this paper, we establish weak convergence of QRP in a general series approximation framework, which includes l...

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets which are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently Kleiner, Talwalkar, Sarkar...

We investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty, when several competing regression models are available to describe the dose response relationship. The proposed approach uses the complete structure of the regression models, but does not require knowledge of the parameters of the competing mo...

This paper investigates the problem if the difference between two parametric models $m_1, m_2$ describing the relation between the response and covariates in two groups is of no practical significance, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses $H_0: d(m_1,m_2)...

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop asymptotic theory for estimators of dependence measures or copula densities, they allow to derive tests for stochasti...

This article is concerned with confidence interval construction for functionals of the survival distribution for censored dependent data. We adopt the recently developed self-normalization approach (Shao, 2010), which does not involve consistent estimation of the asymptotic variance, as implicitly used in the blockwise empirical likelihood approach...

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions equipped with the supremum metric. However, there are cases when weak convergence in those spaces fails to hold. E...

In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecificat...

Classical spectral methods are subject to two fundamental limitations: they only can ac- count for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted recently to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, methods relax...

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt;Xt-k) in a process (Xt)t2Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis)...

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt;Xt-k) in a process (Xt)t2Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis)...

In a recent paper Noh et al. (2013) proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This paper investigates the effect which occurs under misspecification of the paramet...

The speed of computations in neocortical networks critically depends on the ability of populations of spiking neurons to rapidly detect subtle changes in the input and translate them into firing rate changes. However, high sensitivity to perturbations may lead to explosion of noise and increased energy consumption. Can neuronal networks reconcile t...

We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak conv...

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the present paper we extend his main result to the case of serial dependent random variables by...

In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such statistics is challenging since it typically involves a nontrivial verification of technical conditions and tedious c...

A new test for comparing conditional quantile curves is proposed which is able to detect Pitman alternatives converging to the null hypothesis at the optimal rate. The basic idea of the test is to measure differences between the curves by a process of integrated nonparametric estimates of the quantile curve. We prove weak convergence of this proces...

In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for the properly standardized empirical quantile process and discover some surprising differences wit...

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(\alpha) tests, as in Neyman(1959), and shown to be locally, asymptotically optimal. A unified a...

This study analyzes the impact of German codetermination rights on overtime hours. Using German personal data, our results show that the effects of works councils strongly depend on the contracted working time. Furthermore, we find a strong heterogeneity in the effects of works councils across different quantiles of the overtime hours distribution....

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fr\'echet-upper bound. We prove weak convergence of thi...

We consider the problem of detecting a dose response signal if several competing regression models are available to describe the dose response relationship. In particular, we re-analyze the MCP-Mod approach from Bretz et al. (2005), which has become a very popular tool for this problem in recent years. We propose an improvement based on likelihood...

We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile regression model is large. It is demonstrated that traditional penalized estimators such as the adaptive lasso yield...

We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakl...

In this paper we discuss the asymptotic properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we a...

In this paper we discuss the asymptotical properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we...

In this paper we present an alternative method for the spectral analysis of a strictly stationary time series (Yt)eZ. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs (Yt; Yt-k) and the independence copula. This object is called copula spectral density kernel and allows to separate marginal and ser...

In this paper we present an alternative method for the spectral analysis of a strictly stationary time series $\{Y_t\}_{t\in \Z}$. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This object is called {\it copula spectral density kernel} and allows to s...

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the present paper we extend his main result to the case of serial dependent random variables by...

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-upper bound. We prove weak convergence of this...

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function $A^*(t)$, which minimizes a weighted $L^2$-distance between the logarithm of the copula $C(y^{1-t},y^t)$ and functions of the form $A(t)\log(y)$ is derived. If the un...

A new test for comparing conditional quantile curves is proposed which is able to detect Pitman alternatives converging to the null hypothesis at the optimal rate. The basic idea of the test is to measure differences between the curves by a process of integrated non parametric estimates of the quantile curve. We prove weak convergence of this proce...

Visual stimulation often leads to elevated fluctuations of the membrane potential in the γ-frequency range (25-70 Hz) in visual cortex neurons. Recently, we have found that the strength of γ-band fluctuations is coupled to the oscillation of the membrane potential at the temporal frequency of the stimulus, so that the γ-band fluctuations are strong...

We consider the problem of testing the equality of J quantile curves from independent samples. A test statistic based on an L 2-distance between non-crossing non-parametric estimates of the quantile curves from the individual samples is proposed. Asymptotic normality of this statistic is established under the null hypothesis, local and fixed altern...

We propose a new class of estimators for Pickands dependence function which is based on the best L2-approximation of the logarithm of the copula by logarithms of extreme-value copulas. An explicit integral representation of the best approximation is derived and it is shown that this approximation satisfies the boundary conditions of a Pickands depe...

We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak conv...

We consider the problem of testing the equality of J quantile curves from independent samples. A test statistic based on an L^2-distance between non-crossing nonparametric estimates of the quantile curves from the individual samples is proposed. Asymptotic normality of this statistic is established under the null hypothesis, local and fixed alterna...

[This corrects the article on p. e1962 in vol. 3, PMID: 18398478.].

Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various "p"  is an element of  (0, 1)). We propose a new non-parametric estimate of conditional quantiles that avoids th...

The generation of action potentials (APs) is a key process in the operation of nerve cells and the communication between neurons. Action potentials in mammalian central neurons are characterized by an exceptionally fast onset dynamics, which differs from the typically slow and gradual onset dynamics seen in identified snail neurons. Here we describ...

In this paper a new nonparametric estimate of conditional quantiles is proposed, that avoids the problem of crossing quantile curves [calculated for various p ist Element von (0; 1)]: The method uses an initial estimate of the conditional distribution function in a first step and solves the problem of inversion and monotonization with respect to p...