Material for “ Weighted Likelihood Estimation under Two - Phase Sampling
نویسندگان
چکیده
A. Appendix. We repeatedly use the notation for empirical measures and processes introduced in Section 2 following [2]. The fundamental idea of [2] is to view Gξj,Nj as the exchangeably weighted bootstrap empirical process corresponding to Gj,Nj ≡ √ Nj ( Pj,Nj − P0|j ) for j = 1, . . . , J . The processes Gξj,Nj converge weakly to √ pj(1− pj)Gj for independent P0|jBrownian bridge processes Gj , j = 1, . . . , J , in `∞(F) for Donsker classes F . Asymptotic linearity and the limiting distributions of α̂N in binary regression and (modified and centered) calibration are given by the following proposition. The proof requires a Glivenko-Cantelli theorem for PN whose proof is independent of Proposition A.1.
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Weighted Likelihood Estimation under Two-phase Sampling.
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