Correlation Theory of Stationary and Related Random Functions
Correlation Theory of Stationary and Related Random Functions

Author: A.M. Yaglom

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 267

ISBN-13: 1461246288

DOWNLOAD EBOOK

Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.

The Jackknife and Bootstrap
The Jackknife and Bootstrap

Author: Jun Shao

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 533

ISBN-13: 1461207959

DOWNLOAD EBOOK

The jackknife and bootstrap are the most popular data-resampling meth ods used in statistical analysis. The resampling methods replace theoreti cal derivations required in applying traditional methods (such as substitu tion and linearization) in statistical analysis by repeatedly resampling the original data and making inferences from the resamples. Because of the availability of inexpensive and fast computing, these computer-intensive methods have caught on very rapidly in recent years and are particularly appreciated by applied statisticians. The primary aims of this book are (1) to provide a systematic introduction to the theory of the jackknife, the bootstrap, and other resampling methods developed in the last twenty years; (2) to provide a guide for applied statisticians: practitioners often use (or misuse) the resampling methods in situations where no theoretical confirmation has been made; and (3) to stimulate the use of the jackknife and bootstrap and further devel opments of the resampling methods. The theoretical properties of the jackknife and bootstrap methods are studied in this book in an asymptotic framework. Theorems are illustrated by examples. Finite sample properties of the jackknife and bootstrap are mostly investigated by examples and/or empirical simulation studies. In addition to the theory for the jackknife and bootstrap methods in problems with independent and identically distributed (Li.d.) data, we try to cover, as much as we can, the applications of the jackknife and bootstrap in various complicated non-Li.d. data problems.

Geostatistics
Geostatistics

Author: Jean-Paul Chilès

Publisher: John Wiley & Sons

Published: 2009-09-25

Total Pages: 718

ISBN-13: 0470317833

DOWNLOAD EBOOK

A novel, practical approach to modeling spatial uncertainty. This book deals with statistical models used to describe natural variables distributed in space or in time and space. It takes a practical, unified approach to geostatistics-integrating statistical data with physical equations and geological concepts while stressing the importance of an objective description based on empirical evidence. This unique approach facilitates realistic modeling that accounts for the complexity of natural phenomena and helps solve economic and development problems-in mining, oil exploration, environmental engineering, and other real-world situations involving spatial uncertainty. Up-to-date, comprehensive, and well-written, Geostatistics: Modeling Spatial Uncertainty explains both theory and applications, covers many useful topics, and offers a wealth of new insights for nonstatisticians and seasoned professionals alike. This volume: * Reviews the most up-to-date geostatistical methods and the types of problems they address. * Emphasizes the statistical methodologies employed in spatial estimation. * Presents simulation techniques and digital models of uncertainty. * Features more than 150 figures and many concrete examples throughout the text. * Includes extensive footnoting as well as a thorough bibliography. Geostatistics: Modeling Spatial Uncertainty is the only geostatistical book to address a broad audience in both industry and academia. An invaluable resource for geostatisticians, physicists, mining engineers, and earth science professionals such as petroleum geologists, geophysicists, and hydrogeologists, it is also an excellent supplementary text for graduate-level courses in related subjects.

Linear Models
Linear Models

Author: C.Radhakrishna Rao

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 360

ISBN-13: 1489900241

DOWNLOAD EBOOK

The book is based on both authors' several years of experience in teaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results about the definiteness of matrices, especially for the differences of matrices, which enable superiority comparisons of two biased estimates to be made for the first time. We have attempted to provide a unified theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss func tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and its practical applica tions will be useful not only to students but also to researchers and con sultants in statistics.

Statistical Tools for Nonlinear Regression
Statistical Tools for Nonlinear Regression

Author: Sylvie Huet

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 161

ISBN-13: 147572523X

DOWNLOAD EBOOK

Statistical Tools for Nonlinear Regression presents methods for analyzing data. It has been expanded to include binomial, multinomial and Poisson non-linear models. The examples are analyzed with the free software nls2 updated to deal with the new models included in the second edition. The nls2 package is implemented in S-PLUS and R. Several additional tools are included in the package for calculating confidence regions for functions of parameters or calibration intervals, using classical methodology or bootstrap.

Advanced Statistics
Advanced Statistics

Author: Shelby J. Haberman

Publisher: Springer Science & Business Media

Published: 1996-06-20

Total Pages: 520

ISBN-13: 9780387947174

DOWNLOAD EBOOK

Advanced Statistics provides a rigorous development of statistics that emphasizes the definition and study of numerical measures that describe population variables. Volume 1 studies properties of commonly used descriptive measures. Volume 2 considers use of sampling from populations to draw inferences concerning properties of populations. The volumes are intended for use by graduate students in statistics and professional statisticians, although no specific prior knowledge of statistics is assumed. The rigorous treatment of statistical concepts requires that the reader be familiar with mathematical analysis and linear algebra, so that open sets, continuous functions, differentials, Raman integrals, matrices, and vectors are familiar terms.

Weak Convergence and Empirical Processes
Weak Convergence and Empirical Processes

Author: Aad van der vaart

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 523

ISBN-13: 1475725450

DOWNLOAD EBOOK

This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

Test Equating
Test Equating

Author: Michael J. Kolen

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 351

ISBN-13: 1475724128

DOWNLOAD EBOOK

In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques. This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved. The main themes are: - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating. The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented. As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for the first time as part of their graduate study will find this an invaluable text and reference.