## A First Course on Parametric Inference

Author: Balvant Keshav Kale
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842652190
Page: 295
View: 9373
Starting with the basic concept of sufficient statistics, this text uses the classical approach based on minimum variance to provide an understanding of unbiased estimation.

## STATISTICAL INFERENCE : THEORY OF ESTIMATION

Author: MANOJ KUMAR SRIVASTAVA,ABDUL HAMID KHAN,NAMITA SRIVASTAVA
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812034930X
Category: Mathematics
Page: 808
View: 9319
This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.

## A First Course in Statistics for Signal Analysis

Author: Wojbor A. Woyczynski
Publisher: Springer Science & Business Media
ISBN: 9780817681012
Category: Mathematics
Page: 261
View: 4669
This self-contained and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, which are explained in a concise, yet rigorous presentation. With abundant practice exercises and thorough explanations, A First Course in Statistics for Signal Analysis is an excellent tool for both teaching students and training laboratory scientists and engineers. Improvements in the second edition include considerably expanded sections, enhanced precision, and more illustrative figures.

## Journal of the American Statistical Association

Author: N.A
Publisher: N.A
ISBN: N.A
Category: Statistics
Page: N.A
View: 3549

## A First Course in Order Statistics

Author: Barry C. Arnold,N. Balakrishnan,H. N. Nagaraja
Publisher: SIAM
ISBN: 0898716489
Category: Mathematics
Page: 279
View: 9334
This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.

## An Introduction to Stochastic Process

Publisher: CRC Press
ISBN: 9780849309915
Category: Mathematics
Page: 224
View: 9578
Designed for college mathematics students at all levels, this book grew from the author's lectures for advanced undergraduate courses at Canadian and United States universities, and from a postgraduate course at Calcutta University. It introduces discrete time Markov chain and second order stochastic analysis, and includes discussions of renewal theory, time series analysis, queuing theory, Brownian motions, and martingale theorems.

## A First Course in Linear Model Theory

Author: Nalini Ravishanker,Dipak K. Dey
Publisher: CRC Press
ISBN: 9781584882473
Category: Mathematics
Page: 496
View: 4563
This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

## The British National Bibliography

Author: Arthur James Wells
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 2373

## Examples in Parametric Inference with R

Author: Ulhas Jayram Dixit
Publisher: Springer
ISBN: 9811008892
Category: Mathematics
Page: 423
View: 9748
This book discusses examples in parametric inference with R. Combining basic theory with modern approaches, it presents the latest developments and trends in statistical inference for students who do not have an advanced mathematical and statistical background. The topics discussed in the book are fundamental and common to many fields of statistical inference and thus serve as a point of departure for in-depth study. The book is divided into eight chapters: Chapter 1 provides an overview of topics on sufficiency and completeness, while Chapter 2 briefly discusses unbiased estimation. Chapter 3 focuses on the study of moments and maximum likelihood estimators, and Chapter 4 presents bounds for the variance. In Chapter 5, topics on consistent estimator are discussed. Chapter 6 discusses Bayes, while Chapter 7 studies some more powerful tests. Lastly, Chapter 8 examines unbiased and other tests. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability, will greatly benefit from this book. Students are expected to know matrix algebra, calculus, probability and distribution theory before beginning this course. Presenting a wealth of relevant solved and unsolved problems, the book offers an excellent tool for teachers and instructors who can assign homework problems from the exercises, and students will find the solved examples hugely beneficial in solving the exercise problems.

## A First Course in Multivariate Statistics

Author: Bernard Flury
Publisher: Springer Science & Business Media
ISBN: 1475727658
Category: Mathematics
Page: 715
View: 6241
A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis.

## Statistical Analysis of Panel Count Data

Author: Jianguo Sun,Xingqiu Zhao
Publisher: Springer Science & Business Media
ISBN: 1461487153
Category: Medical
Page: 271
View: 7250
Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that can occur or happen multiple times or repeatedly. Examples of recurrent events include disease infections, hospitalizations in medical studies, warranty claims of automobiles or system break-downs in reliability studies. In fact, many other fields yield event history data too such as demographic studies, economic studies and social sciences. For the cases where the study subjects are observed continuously, the resulting data are usually referred to as recurrent event data. This book collects and unifies statistical models and methods that have been developed for analyzing panel count data. It provides the first comprehensive coverage of the topic. The main focus is on methodology, but for the benefit of the reader, the applications of the methods to real data are also discussed along with numerical calculations. There exists a great deal of literature on the analysis of recurrent event data. This book fills the void in the literature on the analysis of panel count data. This book provides an up-to-date reference for scientists who are conducting research on the analysis of panel count data. It will also be instructional for those who need to analyze panel count data to answer substantive research questions. In addition, it can be used as a text for a graduate course in statistics or biostatistics that assumes a basic knowledge of probability and statistics.

## Bootstrapping

A Nonparametric Approach to Statistical Inference
Author: Christopher Z. Mooney,Robert D. Duval,Robert Duvall
Publisher: SAGE
ISBN: 9780803953819
Category: Social Science
Page: 73
View: 505
Bootstrapping, a computational nonparametric technique for "re-sampling," enables researchers to draw a conclusion about the characteristics of a population strictly from the existing sample rather than by making parametric assumptions about the estimator. Using real data examples from per capita personal income to median preference differences between legislative committee members and the entire legislature, Mooney and Duval discuss how to apply bootstrapping when the underlying sampling distribution of the statistics cannot be assumed normal, as well as when the sampling distribution has no analytic solution. In addition, they show the advantages and limitations of four bootstrap confidence interval methods: normal approximation, percenti

## Proceedings

Author: American Institute for Decision Sciences. Meeting
Publisher: N.A
ISBN: N.A
Category: Decision making
Page: N.A
View: 4871

## Mathematical Reviews

Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 4170

## Introduction to the Theory of Statistical Inference

Author: Hannelore Liero,Silvelyn Zwanzig
Publisher: CRC Press
ISBN: 1466503203
Category: Mathematics
Page: 284
View: 2650
Based on the authors’ lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems. Highlights Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form Classroom-tested and designed for students of mathematical statistics Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material Solutions provided for problems formulated at the end of each chapter Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models Theoretical, difficult, or frequently misunderstood problems are marked The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

## Experimental Design and Statistics for Psychology

A First Course
Author: Fabio Sani,John Todman
Publisher: John Wiley & Sons
ISBN: 1405150386
Category: Psychology
Page: 240
View: 1605
Experimental Design and Statistics for Psychology: A First Course is a concise, straighforward and accessible introduction to the design of psychology experiments and the statistical tests used to make sense of their results. Makes abundant use of charts, diagrams and figures. Assumes no prior knowledge of statistics. Invaluable to all psychology students needing a firm grasp of the basics, but tackling of some of the topic’s more complex, controversial issues will also fire the imagination of more ambitious students. Covers different aspects of experimental design, including dependent versus independent variables, levels of treatment, experimental control, random versus systematic errors, and within versus between subjects design. Provides detailed instructions on how to perform statistical tests with SPSS. Downloadable instructor resources to supplement and support your lectures can be found at www.blackwellpublishing.com/sani and include sample chapters, test questions, SPSS data sets, and figures and tables from the book.

## Statistical Methodology Reviews

Author: Oscar Krisen Buros
Publisher: N.A
ISBN: N.A
Category: Research
Page: N.A
View: 9666

## Applied Asymptotics

Case Studies in Small-Sample Statistics
Author: A. R. Brazzale,A. C. Davison,N. Reid
Publisher: Cambridge University Press
ISBN: 9780521847032
Page: 236
View: 1260