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This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and…

Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion…

This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is…

Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional…

In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…

In this paper, we propose a novel approach for tackling the obstacles of empirical likelihood in the face of massive data, which is called split sample mean empirical likelihood (SSMEL), our approach provides a unique perspective for…

We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models. Specifically, nonparametric Bayesian inferences are separately performed on each subset randomly split from a massive…

We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted,…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…

In multi-center clinical trials, due to various reasons, the individual-level data are strictly restricted to be assessed publicly. Instead, the summarized information is widely available from published results. With the advance of…

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…

We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true likelihood function. Our approach is built on empirical likelihood, a non-parametric approximation…

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in…

The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…

It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…

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,…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…

Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…