Nonparametric Goodness of Fit Testing Under Gaussian Models

Author: Yuri Ingster
Publisher: Springer Science & Business Media
ISBN: 9780387215808
Release Date: 2012-11-12
Genre: Mathematics

This book presents the modern theory of nonparametric goodness-of-fit testing. It fills the gap in modern nonparametric statistical theory by discussing hypothesis testing and addresses mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems relevant in signal detection and transmission and in technical and medical diagnostics among others.

Nonlinear Estimation and Classification

Author: David D. Denison
Publisher: Springer Science & Business Media
ISBN: 9780387215792
Release Date: 2013-11-11
Genre: Mathematics

Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data. This is due in part to recent advances in data collection and computing technologies. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing. The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics. The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future.

Parametric and Nonparametric Inference from Record Breaking Data

Author: Sneh Gulati
Publisher: Springer Science & Business Media
ISBN: 9780387215495
Release Date: 2013-03-14
Genre: Mathematics

By providing a comprehensive look at statistical inference from record-breaking data in both parametric and nonparametric settings, this book treats the area of nonparametric function estimation from such data in detail. Its main purpose is to fill this void on general inference from record values. Statisticians, mathematicians, and engineers will find the book useful as a research reference. It can also serve as part of a graduate-level statistics or mathematics course.

Block Designs A Randomization Approach

Author: Tadeusz Calinski
Publisher: Springer Science & Business Media
ISBN: 9781441992468
Release Date: 2012-12-06
Genre: Mathematics

The book is composed of two volumes, each consisting of five chapters. In Vol ume I, following some statistical motivation based on a randomization model, a general theory of the analysis of experiments in block designs has been de veloped. In the present Volume II, the primary aim is to present methods of that satisfy the statistical requirements described in constructing block designs Volume I, particularly those considered in Chapters 3 and 4, and also to give some catalogues of plans of the designs. Thus, the constructional aspects are of predominant interest in Volume II, with a general consideration given in Chapter 6. The main design investigations are systematized by separating the material into two contents, depending on whether the designs provide unit efficiency fac tors for some contrasts of treatment parameters (Chapter 7) or not (Chapter 8). This distinction in classifying block designs may be essential from a prac tical point of view. In general, classification of block designs, whether proper or not, is based here on efficiency balance (EB) in the sense of the new termi nology proposed in Section 4. 4 (see, in particular, Definition 4. 4. 2). Most of the attention is given to connected proper designs because of their statistical advantages as described in Volume I, particularly in Chapter 3. When all con trasts are of equal importance, either the class of (v - 1; 0; O)-EB designs, i. e.

Topics in Stochastic Analysis and Nonparametric Estimation

Author: Pao-Liu Chow
Publisher: Springer Science & Business Media
ISBN: 9780387751115
Release Date: 2010-07-19
Genre: Mathematics

To honor Rafail Z. Khasminskii, on his seventy-fifth birthday, for his contributions to stochastic processes and nonparametric estimation theory an IMA participating institution conference entitled "Conference on Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation, and Related Problems" was held. This volume commemorates this special event. Dedicated to Professor Khasminskii, it consists of nine papers on various topics in probability and statistics.

Nonparametric Monte Carlo Tests and Their Applications

Author: Li-Xing Zhu
Publisher: Springer Science & Business Media
ISBN: 9780387290539
Release Date: 2006-04-09
Genre: Mathematics

A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level. The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations. Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests. Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics. From the reviews: "These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. ... The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. ... this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006 "...Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006

Introduction to Nonparametric Estimation

Author: Alexandre B. Tsybakov
Publisher: Springer Science & Business Media
ISBN: 9780387790527
Release Date: 2008-10-22
Genre: Mathematics

Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.

Introduction to Statistics for Biomedical Engineers

Author: Kristina M. Ropella
Publisher: Morgan & Claypool Publishers
ISBN: 9781598291964
Release Date: 2007
Genre: Mathematics

There are many books written about statistics, some brief, some detailed, some humorous, some colorful, and some quite dry. Each of these texts is designed for a specific audience. Too often, texts about statistics have been rather theoretical and intimidating for those not practicing statistical analysis on a routine basis. Thus, many engineers and scientists, who need to use statistics much more frequently than calculus or differential equations, lack sufficient knowledge of the use of statistics. The audience that is addressed in this text is the university-level biomedical engineering student who needs a bare-bones coverage of the most basic statistical analysis frequently used in biomedical engineering practice. The text introduces students to the essential vocabulary and basic concepts of probability and statistics that are required to perform the numerical summary and statistical analysis used in the biomedical field. This text is considered a starting point for important issues to consider when designing experiments, summarizing data, assuming a probability model for the data, testing hypotheses, and drawing conclusions from sampled data.A student who has completed this text should have sufficient vocabulary to read more advanced texts on statistics and further their knowledge about additional numerical analyses that are used in the biomedical engineering field but are beyond the scope of this text. This book is designed to supplement an undergraduate-level course in applied statistics, specifically in biomedical engineering. Practicing engineers who have not had formal instruction in statistics may also use this text as a simple, brief introduction to statistics used in biomedical engineering. The emphasis is on the application of statistics, the assumptions made in applying the statistical tests, the limitations of these elementary statistical methods, and the errors often committed in using statistical analysis. A number of examples from biomedical engineering research and industry practice are provided to assist the reader in understanding concepts and application. It is beneficial for the reader to have some background in the life sciences and physiology and to be familiar with basic biomedical instrumentation used in the clinical environment.Contents: Introduction / Collecting Data and Experimental Design / Data Summary and Descriptive Statistics / Assuming a Probability Model from the Sample Data / Statistical Inference / Linear Regression and Correlation Analysis / Power Analysis and Sample Size / Just the Beginning / Bibliography