Year: 2013
Type: article
Abstract: We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko–Cantelli theorem, a theorem for rates of convergence of $M$-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling and sampling without replacement at the second phase. Using these general results, we derive asymptotic distributions of the WLE of a finite-dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is estimable either at regular or nonregular rates. We illustrate these results and methods in the Cox model with right censoring and interval censoring. We compare the methods via their asymptotic variances under both sampling without replacement and the more usual (and easier to analyze) assumption of Bernoulli sampling at the second phase.
Source: The Annals of Statistics
DOI: 10.1214/12-aos1073
Authors: Takumi Saegusa, Jon A. Wellner
Institution: University of Washington
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: Statistical Methods in HIV/AIDS Research, G1875133739, G2318551012, Shape Restrictions, Empirical Processes, and Semiparametric Models, Statistical Issues in AIDS Research, A Multiplatform Approach to Develop ENL-Targeting Molecules as Drug Candidates for Acute Myeloid Leukemia, Statistical Issues in AIDS Research
OpenAlex ID: W971128976