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'
نویسندگان
چکیده
We state and prove a limit theorem for estimators of a general, possibly infinite dimensional parameter based on unbiased estimating equations containing estimated nuisance parameters. The theorem corrects a gap in the proof of one of the assertions of our paper 'Weighted likelihood for semiparametric models and two-phase stratified samples, with application to Cox regression'.
منابع مشابه
Weighted Likelihood for Semiparametric Models and Two-phase Stratified Samples, with Application to Cox Regression
Weighted likelihood, in which one solves Horvitz-Thompson or inverse probability weighted (IPW) versions of the likelihood equations, offers a simple and robust method for fitting models to two phase stratified samples. We consider semiparametric models for which solution of infinite dimensional estimating equations leads to √ N consistent and asymptotically Gaussian estimators of both Euclidea...
متن کاملA Sieve M-theorem for Bundled Parameters in Semiparametric Models, with Application to the Efficient Estimation in a Linear Model for Censored Data By
In many semiparametric models that are parameterized by two types of parameters—a Euclidean parameter of interest and an infinite-dimensional nuisance parameter—the two parameters are bundled together, that is, the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the u...
متن کاملA Sieve M-theorem for Bundled Parameters in Semiparametric Models, with Application to the Efficient Estimation in a Linear Model for Censored Data.
In many semiparametric models that are parameterized by two types of parameters - a Euclidean parameter of interest and an infinite-dimensional nuisance parameter, the two parameters are bundled together, i.e., the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the u...
متن کاملWeighted Likelihood Estimation under Two-phase Sampling.
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko-Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probabi...
متن کاملZ-estimation and stratified samples: application to survival models.
The infinite dimensional Z-estimation theorem offers a systematic approach to joint estimation of both Euclidean and non-Euclidean parameters in probability models for data. It is easily adapted for stratified sampling designs. This is important in applications to censored survival data because the inverse probability weights that modify the standard estimating equations often depend on the ent...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Scandinavian journal of statistics, theory and applications
دوره 35 1 شماره
صفحات -
تاریخ انتشار 2008