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Zbl 1164.62012
Beslow, Norman E.; Wellner, Jon A.
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)
[J] Scand. J. Stat. 35, No. 1, 186-192 (2008). ISSN 0303-6898; ISSN 1467-9469/e

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.
[R. E. Maiboroda (Ky\"iv)]

MSC 2000:: *62G20 Nonparametric asymptotic efficiency
62G05 Nonparametric estimation
62D05 Statistical sampling theory
62G08 Nonparametric regression

Keywords: nuisance parameter; asymptotic distribution; estimating equation

Citations: Zbl 1142.62014

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