Large Sample Theory of Empirical Distributions in Biased Sampling Models

摘要

The Vardi (1985) s - sample model for biased sampling is studied. The large sample behavior of the nonparametric maximum likelihood estimator Gn, including results on uniform consistency of Gn, convergence of rtn (Gn - G) to a Gaussian process, and asymptotic efficiency of Gn as an estimator of G is discussed. The proofs are based upon results for empirical processes indexed by sets and functions, properties of irreducible M-matrices, and the homotopy invariance theorem. Applications to stratified sampling, choice-based sampling in econometrics, and case-control studies in biostatistics are discussed.