Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference
Author: Michael R. Kosorok
Publisher: Springer Science & Business Media
Total Pages: 482
Release: 2007-12-29
Genre: Mathematics
ISBN: 0387749780

Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Asymptotic Statistics

Asymptotic Statistics
Author: A. W. van der Vaart
Publisher: Cambridge University Press
Total Pages: 470
Release: 2000-06-19
Genre: Mathematics
ISBN: 9780521784504

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.

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.

Statistical Properties of the Generalized Inverse Gaussian Distribution

Statistical Properties of the Generalized Inverse Gaussian Distribution
Author: B. Jorgensen
Publisher: Springer Science & Business Media
Total Pages: 197
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461256984

In 1978 the idea of studying the generalized inverse Gaussian distribution was proposed to me by Professor Ole Barndorff-Nielsen, who had come across the distribution in the study of the socalled hyperbolic distributions where it emerged in connection with the representation of the hyperbolic distributions as mixtures of normal distributions. The statistical properties of the generalized inverse Gaussian distribution were at that time virtually unde veloped, but it turned out that the distribution has some nice properties, and models many sets of data satisfactorily. This work contains an account of the statistical properties of the distribu tion as far as they are developed at present. The work was done at the Department of Theoretical Statistics, Aarhus University, mostly in 1979, and was partial fulfilment to wards my M. Sc. degree. I wish to convey my warm thanks to Ole Barn dorff-Nielsen and Preben BI~sild for their advice and for comments on earlier versions of the manuscript and to Jette Hamborg for her skilful typing.

Semiparametric Modeling of Implied Volatility

Semiparametric Modeling of Implied Volatility
Author: Matthias R. Fengler
Publisher: Springer Science & Business Media
Total Pages: 232
Release: 2005-12-19
Genre: Business & Economics
ISBN: 3540305912

This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.

Statistical Causal Inferences and Their Applications in Public Health Research

Statistical Causal Inferences and Their Applications in Public Health Research
Author: Hua He
Publisher: Springer
Total Pages: 324
Release: 2016-10-26
Genre: Medical
ISBN: 3319412590

This book compiles and presents new developments in statistical causal inference. The accompanying data and computer programs are publicly available so readers may replicate the model development and data analysis presented in each chapter. In this way, methodology is taught so that readers may implement it directly. The book brings together experts engaged in causal inference research to present and discuss recent issues in causal inference methodological development. This is also a timely look at causal inference applied to scenarios that range from clinical trials to mediation and public health research more broadly. In an academic setting, this book will serve as a reference and guide to a course in causal inference at the graduate level (Master's or Doctorate). It is particularly relevant for students pursuing degrees in statistics, biostatistics, and computational biology. Researchers and data analysts in public health and biomedical research will also find this book to be an important reference.

Empirical Processes

Empirical Processes
Author: David Pollard
Publisher: IMS
Total Pages: 100
Release: 1990
Genre: Distribution (Probability theory).
ISBN: 9780940600164

Probability for Statistics and Machine Learning

Probability for Statistics and Machine Learning
Author: Anirban DasGupta
Publisher: Springer Science & Business Media
Total Pages: 796
Release: 2011-05-17
Genre: Mathematics
ISBN: 1441996346

This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

Asymptotic Theory of Statistical Inference for Time Series

Asymptotic Theory of Statistical Inference for Time Series
Author: Masanobu Taniguchi
Publisher: Springer
Total Pages: 0
Release: 2012-10-23
Genre: Mathematics
ISBN: 9781461270287

The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Mixed Effects Models for Complex Data

Mixed Effects Models for Complex Data
Author: Lang Wu
Publisher: CRC Press
Total Pages: 431
Release: 2009-11-11
Genre: Mathematics
ISBN: 9781420074086

Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.