Efficient and Adaptive Estimation for Semiparametric Models

Efficient and Adaptive Estimation for Semiparametric Models
Author: Peter J. Bickel
Publisher: Springer
Total Pages: 588
Release: 1998-06-01
Genre: Mathematics
ISBN: 0387984739


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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.

Estimation in Semiparametric Models

Estimation in Semiparametric Models
Author: Johann Pfanzagl
Publisher: Springer Science & Business Media
Total Pages: 116
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461233968


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Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.

Nonparametric and Semiparametric Models

Nonparametric and Semiparametric Models
Author: Wolfgang Karl Härdle
Publisher: Springer Science & Business Media
Total Pages: 317
Release: 2012-08-27
Genre: Mathematics
ISBN: 364217146X


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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.

Semiparametric Regression

Semiparametric Regression
Author: David Ruppert
Publisher: Cambridge University Press
Total Pages: 408
Release: 2003-07-14
Genre: Mathematics
ISBN: 9780521785167


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Even experts on semiparametric regression should find something new here.

Semiparametric Theory and Missing Data

Semiparametric Theory and Missing Data
Author: Anastasios Tsiatis
Publisher: Springer Science & Business Media
Total Pages: 392
Release: 2007-01-15
Genre: Mathematics
ISBN: 0387373454


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This book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.

Semiparametric Methods in Econometrics

Semiparametric Methods in Econometrics
Author: Joel L. Horowitz
Publisher: Springer Science & Business Media
Total Pages: 211
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461206219


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Many econometric models contain unknown functions as well as finite- dimensional parameters. Examples of such unknown functions are the distribution function of an unobserved random variable or a transformation of an observed variable. Econometric methods for estimating population parameters in the presence of unknown functions are called "semiparametric." During the past 15 years, much research has been carried out on semiparametric econometric models that are relevant to empirical economics. This book synthesizes the results that have been achieved for five important classes of models. The book is aimed at graduate students in econometrics and statistics as well as professionals who are not experts in semiparametic methods. The usefulness of the methods will be illustrated with applications that use real data.

Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life

Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life
Author: M.S. Nikulin
Publisher: Springer Science & Business Media
Total Pages: 566
Release: 2013-11-11
Genre: Mathematics
ISBN: 0817682066


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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.