A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data

Details A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data

2012-03-12

arxiv.org/abs/1203.2470v1

Annals of Statistics 2011, Vol. 39, No. 6, 3032-3061

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS934 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS934

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 unspecified error distribution function involves the regression coefficients. Motivated by developing an efficient estimating method for the regression parameters, we propose a general sieve M-theorem for bundled parameters and apply the theorem to deriving the asymptotic theory for the sieve maximum likelihood estimation in the linear regression model for censored survival data. The numerical implementation of the proposed estimating method can be achieved through the conventional gradient-based search algorithms such as the Newton--Raphson algorithm. We show that the proposed estimator is consistent and asymptotically normal and achieves the semiparametric efficiency bound. Simulation studies demonstrate that the proposed method performs well in practical settings and yields more efficient estimates than existing estimating equation based methods. Illustration with a real data example is also provided.

Affiliated with

Also associated with

No associations

Rating

A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-488252