Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression
By N. E. Breslow, Jon A. Wellner. 2005
393 citations recorded by the source corpus.
Abstract. We consider semiparametric models for which solution of Horvitz–Thompson or inverse probability weighted (IPW) likelihood equations with two‐phase stratified samples leads to consistent and asymptotically Gaussian estimators of both Euclidean and non‐parametric parameters. For Bernoulli (independent and identically distributed) sampling, standard theory shows that the Euclidean parameter estimator is asymptotically linear in the IPW influence function. By proving weak convergence of the IPW empirical process, and borrowing results on weighted bootstrap empirical processes, we derive a parallel asymptotic expansion for finite population stratified sampling. Several of our key results have been derived already for Cox regression with stratified case–cohort and more general survey designs. This paper is intended to help interpret this previous work and to pave the way towards a general Horvitz–Thompson approach to semiparametric inference with data from complex probability samples.
Subfields: Economics and Econometrics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/55ccd4f3c3b1e8edab8c5eecec085dbd5dc03919
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Citations in the corpus
- Bayesian Estimation Under Informative Sampling (2015, positive): “Our empirical distribution construction follows Breslow & Wellner (2007) and incorporates inverse inclusion probability weights, { 1 / π ν i } i = 1 ,..., N ν , to account for the informative sampling design, where δ ( X i ) denotes the Dirac delta function, with probability mass 1 on X i and we…”
- Toward Deconfounding the Effect of Entity Demographics for Question Answering Accuracy (2021, neutral): “tures, Wald statistics (Fahrmeir et al., 2007) estimate p-values.”
- A Z‐theorem with Estimated Nuisance Parameters and Correction Note for ‘Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression’ (2008, neutral): “ Breslow & Wellner (2007) and that the model (V ) for the conditional distribution of given X , V satisfies the hypotheses of theorem 5.39 of van der Vaart (1998).”