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In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of…
We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show…
The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequently used to model matrix-variate data. The tensor normal…
A novel estimation approach for a general class of semi-parametric multivariate time series models is introduced where the conditional mean is modeled through parametric functions. The focus of the estimation is the conditional mean…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
Studies that collect multi-outcome data such as tobacco and alcohol use are becoming increasingly common. In principle, multi-outcomes studies investigate the correlations between outcomes, including, causal links and/or joint…
The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…
We introduce a new class of mean regression estimators -- penalized maximum tangent likelihood estimation -- for high-dimensional regression estimation and variable selection. We first explain the motivations for the key ingredient, maximum…
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document…
Positive continuous outcomes with a point mass at zero are prevalent in biomedical research. To model the point mass at zero and to provide marginalized covariate effect estimates, marginalized two part models (MTP) have been developed for…
Consider an $(L,1)$ random walk in an i.i.d. random environment, whose environment involves certain parameter. We get the maximum likelihood estimator(MLE) of the environment parameter which can be written as functionals of a multitype…
We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F =…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
Many practical data analysis tasks reduce to learning, from observed samples, how a collection of variables depend on each other. A widely used approach is to fit a Gaussian graphical model, which represents the dependence structure as a…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
In this paper, we explore the two-star Exponential Random Graph Model, which is a two parameter exponential family on the space of simple labeled graphs. We introduce auxiliary variables to express the two-star model as a mixture of the…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
For a set of binary response variables, conditional mean models characterize the expected value of a response variable given the others and are popularly applied in longitudinal and network data analyses. The quadratic exponential binary…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…