Semiparametric adaptive estimation under informative sampling

TL;DR

This paper develops a semiparametric optimal estimator for survey data that accounts for informative sampling, improving efficiency over traditional methods by leveraging survey weights as random variables.

Contribution

It introduces a semiparametric efficiency bound and proposes an estimator that is both consistent and asymptotically efficient under informative sampling conditions.

Findings

The proposed estimator achieves efficiency bounds theoretically.

Simulation studies show improved finite sample performance.

Application to Canadian survey data demonstrates practical utility.

Abstract

In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a well-known unbiased, consistent, and asymptotically normal estimator; however, it is not efficient. Thus, this study derives the semiparametric efficiency bound for various target parameters by considering the survey weight as a random variable and consequently proposes a semiparametric optimal estimator with certain working models on the survey weights. The proposed estimator is consistent, asymptotically normal, and efficient in a class of the regular and asymptotically linear estimators. Further, a limited simulation study is conducted to investigate the finite sample performance of the proposed method. The proposed method is applied to the 1999 Canadian Workplace and Employee Survey data.