Open Access
2023 Reweighted nonparametric likelihood inference for linear functionals
Karun Adusumilli, Taisuke Otsu, Chen Qiu
Author Affiliations +
Electron. J. Statist. 17(2): 2810-2848 (2023). DOI: 10.1214/23-EJS2168

Abstract

This paper is concerned with inference on finite dimensional parameters in semiparametric moment condition models, where the moment functionals are linear with respect to unknown nuisance functions. By exploiting this linearity, we reformulate the inference problem via the Riesz representer, and develop a general inference procedure based on nonparametric likelihood. For treatment effect or missing data analysis, the Riesz representer is typically associated with the inverse propensity score even though the scope of our framework is much wider. In particular, we propose a two-step procedure, where the first step computes the projection weights to approximate the Riesz representer, and the second step reweights the moment conditions so that the likelihood increment admits an asymptotically pivotal chi-square calibration. Our reweighting method is naturally extended to inference on missing data, treatment effects, and data combination models, and other semiparametric problems. Simulation and real data examples illustrate usefulness of the proposed method. We note that our reweighting method and theoretical results are limited to linear functionals.

Funding Statement

This research was conducted with support from the Cornell University Center for Advanced Computing.

Citation

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Karun Adusumilli. Taisuke Otsu. Chen Qiu. "Reweighted nonparametric likelihood inference for linear functionals." Electron. J. Statist. 17 (2) 2810 - 2848, 2023. https://doi.org/10.1214/23-EJS2168

Information

Received: 1 May 2022; Published: 2023
First available in Project Euclid: 9 November 2023

Digital Object Identifier: 10.1214/23-EJS2168

Subjects:
Primary: 62G10 , 62G20
Secondary: 62P20

Keywords: linear functional , nonparametric likelihood , Riesz representer

Vol.17 • No. 2 • 2023
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