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Reweighted nonparametric likelihood inference for linear functionals

Adusumilli, Karun, Otsu, Taisuke and Qiu, Chen (2023) Reweighted nonparametric likelihood inference for linear functionals. Electronic Journal of Statistics, 17 (2). 2810 - 2848. ISSN 1935-7524

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Identification Number: 10.1214/23-EJS2168


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.

Item Type: Article
Official URL:
Additional Information: © 2023 Institute of Mathematical Statistics and the Bernoulli Society
Divisions: Economics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 11 Sep 2023 10:09
Last Modified: 19 May 2024 01:36

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