Related papers: Unified estimation framework for unnormalized mode…

Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…

Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…

The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

We propose a novel targeted maximum likelihood estimator (TMLE) for quantiles in semiparametric missing data models. Our proposed estimator is locally efficient, $\sqrt{n}$-consistent, asymptotically normal, and doubly robust, under…

The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…