Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates.

ABSTRACT: We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widely assumed in the dimension reduction literature is not necessary for methodological or theoretical development: it contributes only to the simplification of non-optimal consistent estimation. We also find that the performance of the usual weighted least square type of estimators deteriorates when the non-parametric component is badly estimated. However, estimators in our family automatically provide

SUBMITTER: Ma Y 

PROVIDER: S-EPMC3747813 | biostudies-literature | 2013 Mar

REPOSITORIES: biostudies-literature