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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’. (English) Zbl 1164.62012
This paper fills the gap in the proof of asymptotic normality of weighted likelihood estimators for parameters fitted to two-phase stratified samples when sampling weights were estimated by the data in the authors’ paper ibid. 34, No. 1, 86–102 (2007; Zbl 1142.62014). The proof is corrected under slightly strengthened assumptions on the theorem. A new theorem on the asymptotic behavior of estimating equations estimates in presence of infinite dimensional nuisance parameters is used to complete the proof.
MSC:
62G20Nonparametric asymptotic efficiency
62G05Nonparametric estimation
62D05Statistical sampling theory, sample surveys
62G08Nonparametric regression