Johns Hopkins Series in the Mathematical Sciences

1 total work

Efficient and Adaptive Estimation for Semiparametric Models

by Peter J. Bickel, etc., Chris A.J. Klaassen, Yaacov Ritov, and Jon A. Wellner

Published 1 September 1993

Wherever statistics is applied, the need to combine interpretable structure with a minimum of assumptions about random fluctuations leads to the use of semiparametric models. In theories of economic choice, for instance, decision making is modeled in part by parametric relations suggested by economic theory and in part by individual fluctuations about which little is known or assumed. Another well-known example, the proportional hazards model of survival analysis, permits an arbitrary baseline hazard rate for a human lifetime but postulates that such variables as medical treatment, age and gender act on the baseline only through parametric scaling factors. This book unifies the theory of estimation in such examples. The authors show how the classical information bounds developed for parametric models extend naturally to nonparametric and semiparametric models. They then apply these techniques in as broad a range of models as possible, illustrating the ease with which heuristic calculations of "optimal behaviour" can be carried out.