Easy Maximum Empirical Likelihood Estimation of Linear Functionals Of A Probability Measure With Infinitely Many Constraints

2023/02/28 by Shan Wang, Wang, Shan, Hanxiang Peng +1
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2302.14768

openalex publication_date 2023/02/28 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

Abstract

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and allow the number of constraints to grow with the sample size. Considered are three cases of information which can be characterized by infinitely many constraints: (1) the marginal distributions are known, (2) the marginals are unknown but identical, and (3) distributional symmetry. An improved spatial depth function is defined and its asymptotic properties are studied. Simulation results on efficiency gain are reported.

Related

• Improving Estimation Efficiency In Structural Equation Models By An Easy Empirical Likelihood Approach
• Statistical learning for constrained functional parameters in infinite-dimensional models with applications in fair machine learning
• Estimation and tests for models satisfying linear constraints with unknown parameter
• Maximum Likelihood under constraints: Degeneracies and Random Critical Points
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency