Semiparametric adaptive estimation under informative sampling
Kosuke Morikawa, Yoshikazu Terada, Jae Kwang Kim
The Annals of Statistics · 2025 · Volume 53 · Issue 3
Abstract
In probability sampling, sampling weights are often used to remove selection bias in the sample. The Horvitz–Thompson estimator is well known to be consistent and asymptotically normally distributed; however, it is not necessarily efficient. This study derives the semiparametric efficiency bound for various target parameters by considering the survey weights as random variables and consequently proposes two semiparametric estimators with working models on the survey weights. One estimator assumes a reasonable parametric working model, but the other estimator does not require specific working models by using the debiased/double machine learning method. The proposed estimators are consistent, asymptotically normal, and efficient in a class of regular and asymptotically linear estimators. 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.
Keywords
62F35, 62G10, 62G20, Double/debiased machine learning, semiparametric efficency bound, weight model
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