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When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…
In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…
This paper proposes IV-based estimators for the semiparametric distribution regression model in the presence of an endogenous regressor, which are based on an extension of IV probit estimators. We discuss the causal interpretation of the…
The present paper deals with a nonparametric M-estimation for right censored regression model with stationary ergodic data. Defined as an implicit function, a kernel type estimator of a family of robust regression is considered when the…
This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…
We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
This paper presents a novel approach to constructing estimators that dominate the classical James-Stein estimator under the quadratic loss for multivariate normal means. Building on Stein's risk representation, we introduce a new sufficient…
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
Stochastic gradient descent (SGD) is an estimation tool for large data employed in machine learning and statistics. Due to the Markovian nature of the SGD process, inference is a challenging problem. An underlying asymptotic normality of…
For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…