Математика
Различные книги в жанре МатематикаComputation for the Analysis of Designed Experiments
Addresses the statistical, mathematical, and computational aspects of the construction of packages and analysis of variance (ANOVA) programs. Includes a disk at the back of the book that contains all program codes in four languages, APL, BASIC, C, and FORTRAN. Presents illustrations of the dual space geometry for all designs, including confounded designs.
Survival Models and Data Analysis
Survival analysis deals with the distribution of life times, essentially the times from an initiating event such as birth or the start of a job to some terminal event such as death or pension. This book, originally published in 1980, surveys and analyzes methods that use survival measurements and concepts, and helps readers apply the appropriate method for a given situation. Four broad sections cover introductions to data, univariate survival function, multiple-failure data, and advanced topics.
Statistical Analysis with Missing Data
Praise for the First Edition of Statistical Analysis with Missing Data «An important contribution to the applied statistics literature.... I give the book high marks for unifying and making accessible much of the past and current work in this important area.» —William E. Strawderman, Rutgers University «This book…provide[s] interesting real-life examples, stimulating end-of-chapter exercises, and up-to-date references. It should be on every applied statistician’s bookshelf.» —The Statistician «The book should be studied in the statistical methods department in every statistical agency.» —Journal of Official Statistics Statistical analysis of data sets with missing values is a pervasive problem for which standard methods are of limited value. The first edition of Statistical Analysis with Missing Data has been a standard reference on missing-data methods. Now, reflecting extensive developments in Bayesian methods for simulating posterior distributions, this Second Edition by two acknowledged experts on the subject offers a thoroughly up-to-date, reorganized survey of current methodology for handling missing-data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe rigorous yet simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing-data mechanism and apply the theory to a wide range of important missing-data problems. The new edition now enlarges its coverage to include: Expanded coverage of Bayesian methodology, both theoretical and computational, and of multiple imputation Analysis of data with missing values where inferences are based on likelihoods derived from formal statistical models for the data-generating and missing-data mechanisms Applications of the approach in a variety of contexts including regression, factor analysis, contingency table analysis, time series, and sample survey inference Extensive references, examples, and exercises Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Statistical Analysis With Missing Data was among those chosen.
Structural Equations with Latent Variables
Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering. It begins with an introduction to basic descriptive and inferential methods for categorical data, and then gives thorough coverage of the most current developments, such as loglinear and logit models for ordinal data. Special emphasis is placed on interpretation and application of methods and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied Regression Analysis Second Edition Norman Draper and Harry Smith Featuring a significant expansion of material reflecting recent advances, here is a complete and up-to-date introduction to the fundamentals of regression analysis, focusing on understanding the latest concepts and applications of these methods. The authors thoroughly explore the fitting and checking of both linear and nonlinear regression models, using small or large data sets and pocket or high-speed computing equipment. Features added to this Second Edition include the practical implications of linear regression; the Durbin-Watson test for serial correlation; families of transformations; inverse, ridge, latent root and robust regression; and nonlinear growth models. Includes many new exercises and worked examples. 1981 (0 471-02995-5) 709 pp.
Nonresponse in Household Interview Surveys
A comprehensive framework for both reduction of nonresponse and postsurvey adjustment for nonresponse This book provides guidance and support for survey statisticians who need to develop models for postsurvey adjustment for nonresponse, and for survey designers and practitioners attempting to reduce unit nonresponse in household interview surveys. It presents the results of an eight-year research program that has assembled an unprecedented data set on respondents and nonrespondents from several major household surveys in the United States. Within a comprehensive conceptual framework of influences on nonresponse, the authors investigate every aspect of survey cooperation, from the influences of household characteristics and social and environmental factors to the interaction between interviewers and householders and the design of the survey itself. Nonresponse in Household Interview Surveys: * Provides a theoretical framework for understanding and studying household survey nonresponse * Empirically explores the individual and combined influences of several factors on nonresponse * Presents chapter introductions, summaries, and discussions on practical implications to clarify concepts and theories * Supplies extensive references for further study and inquiry Nonresponse in Household Interview Surveys is an important resource for professionals and students in survey methodology/research methods as well as those who use survey methods or data in business, government, and academia. It addresses issues critical to dealing with nonresponse in surveys, reducing nonresponse during survey data collection, and constructing statistical compensations for the effects of nonresponse on key survey estimates.
Survey Measurement and Process Quality
An in-depth look at current issues, new research findings, and interdisciplinary exchange in survey methodology and processing Survey Measurement and Process Quality extends the marriage of traditional survey issues and continuous quality improvement further than any other contemporary volume. It documents the current state of the field, reports new research findings, and promotes interdisciplinary exchange in questionnaire design, data collection, data processing, quality assessment, and effects of errors on estimation and analysis. The book's five sections discuss a broad range of issues and topics in each of five major areas, including * Questionnaire design–conceptualization, design of rating scales for effective measurement, self-administered questionnaires, and more * Data collection–new technology, interviewer effects, interview mode, children as respondents * Post-survey processing and operations–modeling of classification operations, coding based on such systems, editing, integrating processes * Quality assessment and control–total quality management, developing current best methods, service quality, quality efforts across organizations * Effects of misclassification on estimation, analysis, and interpretation–misclassification and other measurement errors, new variance estimators that account for measurement error, estimators of nonsampling error components in interview surveys Survey Measurement and Process Quality is an indispensable resource for survey practitioners and managers as well as an excellent supplemental text for undergraduate and graduate courses and special seminars.
A Probabilistic Analysis of the Sacco and Vanzetti Evidence
A Probabilistic Analysis of the Sacco and Vanzetti Evidence is a Bayesian analysis of the trial and post-trial evidence in the Sacco and Vanzetti case, based on subjectively determined probabilities and assumed relationships among evidential events. It applies the ideas of charting evidence and probabilistic assessment to this case, which is perhaps the ranking cause celebre in all of American legal history. Modern computation methods applied to inference networks are used to show how the inferential force of evidence in a complicated case can be graded. The authors employ probabilistic assessment to obtain opinions about how influential each group of evidential items is in reaching a conclusion about the defendants' innocence or guilt. A Probabilistic Analysis of the Sacco and Vanzetti Evidence holds particular interest for statisticians and probabilists in academia and legal consulting, as well as for the legal community, historians, and behavioral scientists. It combines structural and probabilistic ideas in the analysis of masses of evidence from every recognized logical species of evidence. Twenty-eight charts show the chains of reasoning in defense of the relevance of evidentiary matters and a listing of trial witnesses who provided the evidence. References include nearly 300 items drawn from the fields of probability theory, history, law, artificial intelligence, psychology, literature, and other areas.
Geometrical Foundations of Asymptotic Inference
Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following: * Basic properties of curved exponential families * Elements of second-order, asymptotic theory * The Fisher-Efron-Amari theory of information loss and recovery * Jeffreys-Rao information-metric Riemannian geometry * Curvature measures of nonlinearity * Geometrically motivated diagnostics for exponential family regression * Geometrical theory of divergence functions * A classification of and introduction to additional work in the field
A Weak Convergence Approach to the Theory of Large Deviations
Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis–a consistent new approach The theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty. This innovative text demonstrates how to employ the well-established linear techniques of weak convergence theory to prove large deviation results. Beginning with a step-by-step development of the approach, the book skillfully guides readers through models of increasing complexity covering a wide variety of random variable-level and process-level problems. Representation formulas for large deviation-type expectations are a key tool and are developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory and measure-theoretic probability, A Weak Convergence Approach to the Theory of Large Deviations is important reading for both students and researchers.
Hilbert Space Methods in Probability and Statistical Inference
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.