Efficient Estimation In Semiparametric Models

This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis, and related fields. Specific topics covered include: * cancer prognosis using survival forests * short-term health problems related to air pollution: analysis using semiparametric generalized additive models * semiparametric models in the studies of aging and longevity This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.

The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

A smoothed likelihood function is used to construct efficient estimators for some semi-parametric models that contain unknown density functions together with parametric index functions. Smoothing the likelihood makes maximization with respect to the unknown density functions more tractable. The method is used to show the efficiency gains from knowledge of population shares in three cases: (1) binary choice; (2) binary choice when only one outcome is sampled, supplemented by random sampling of the explanatory variables; and (3) linear regression, where the shares are defined by a threshold value of the dependent variable. Semi-parametric efficiency is achieved both for parametric components and for a class of functionals of the error density.