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

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.

Efficient and Adaptive Estimation for Semiparametric Models

Efficient and Adaptive Estimation for Semiparametric Models
Author: Peter J. Bickel
Publisher:
Total Pages: 560
Release: 1993
Genre: Mathematics
ISBN: 9780801845413

Originating with the 1983 Mathematical Sciences Lectures at Johns Hopkins given by Peter J. Bickel and Jon A. Wellner, this volume is about estimation in situations where enough is known to model some features of the data parametrically but not enough is known to assume anything for other features. Such models have arisen in a wide variety of contexts in recent years, particularly in economics, epidemiology, and astronomy. The focus is on asymptotic theory, and the scope is limited to models for independent, identically distributed observations. Annotation c. by Book News, Inc., Portland, Or.

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

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.

Semiparametric Regression

Semiparametric Regression
Author: David Ruppert
Publisher: Cambridge University Press
Total Pages: 410
Release: 2003-07-14
Genre: Mathematics
ISBN: 9780521785167

Semiparametric regression is concerned with the flexible incorporation of non-linear functional relationships in regression analyses. Any application area that benefits from regression analysis can also benefit from semiparametric regression. Assuming only a basic familiarity with ordinary parametric regression, this user-friendly book explains the techniques and benefits of semiparametric regression in a concise and modular fashion. The authors make liberal use of graphics and examples plus case studies taken from environmental, financial, and other applications. They include practical advice on implementation and pointers to relevant software. The 2003 book is suitable as a textbook for students with little background in regression as well as a reference book for statistically oriented scientists such as biostatisticians, econometricians, quantitative social scientists, epidemiologists, with a good working knowledge of regression and the desire to begin using more flexible semiparametric models. Even experts on semiparametric regression should find something new here.

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

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.

Targeted Learning

Targeted Learning
Author: Mark J. van der Laan
Publisher: Springer Science & Business Media
Total Pages: 628
Release: 2011-06-17
Genre: Mathematics
ISBN: 1441997822

The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest. This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.

The Weighted Bootstrap

The Weighted Bootstrap
Author: Philippe Barbe
Publisher: Springer Science & Business Media
Total Pages: 236
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461225329

INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.

Selected Works of Peter J. Bickel

Selected Works of Peter J. Bickel
Author: Jianqing Fan
Publisher: Springer Science & Business Media
Total Pages: 626
Release: 2012-11-28
Genre: Mathematics
ISBN: 1461455448

This volume presents selections of Peter J. Bickel’s major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peter’s amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peter’s life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.

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

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.