Author : B. K. Kale
Publisher : Alpha Science Int'l Ltd.
Page : 284 pages
File Size : 13,50 MB
Release : 1999
Category : Mathematics
ISBN : 9788173191961
Starting with the basic concept of sufficient statistics, the approach based on minimum variance unbiased estimation is presented, in detail, in this text.
Author : Balvant Keshav Kale
Publisher : Alpha Science Int'l Ltd.
Page : 312 pages
File Size : 37,21 MB
Release : 2005
Category : Business & Economics
ISBN : 9781842652190
"After a brief historical perspective, A First Course on Parametric Inference, discusses the basic concept of sufficient statistic and the classical approach based on minimum variance unbiased estimator. There is a separate chapter on simultaneous estimation of several parameters. Large sample theory of estimation, based on consistent asymptotically normal estimators obtained by method of moments, percentile and the method of maximum likelihood is also introduced. The tests of hypotheses for finite samples with classical Neyman-Pearson theory is developed pointing out its connection with Bayesian approach. The hypotheses testing and confidence interval techniques are developed leading to likelihood ratio tests, score tests and tests based on maximum likelihood estimators."--BOOK JACKET.
Author : Larry Wasserman
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 24,53 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 0387217363
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Author : Balvant Keshav Kale
Publisher :
Page : 325 pages
File Size : 37,37 MB
Release : 2015
Category : Parameter estimation
ISBN : 9781842659397
Author : Ulhas Jayram Dixit
Publisher : Springer
Page : 475 pages
File Size : 39,80 MB
Release : 2016-05-20
Category : Mathematics
ISBN : 9811008892
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.
Author : Wojbor A. Woyczyński
Publisher : Springer Nature
Page : 338 pages
File Size : 42,23 MB
Release : 2019-10-04
Category : Mathematics
ISBN : 3030209083
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.
Author : Shelemyahu Zacks
Publisher : Elsevier
Page : 404 pages
File Size : 39,72 MB
Release : 2014-05-20
Category : Mathematics
ISBN : 1483150496
Parametric Statistical Inference: Basic Theory and Modern Approaches presents the developments and modern trends in statistical inference to students who do not have advanced mathematical and statistical preparation. The topics discussed in the book are basic and common to many fields of statistical inference and thus serve as a jumping board for in-depth study. The book is organized into eight chapters. Chapter 1 provides an overview of how the theory of statistical inference is presented in subsequent chapters. Chapter 2 briefly discusses statistical distributions and their properties. Chapter 3 is devoted to the problem of sufficient statistics and the information in samples, and Chapter 4 presents some basic results from the theory of testing statistical hypothesis. In Chapter 5, the classical theory of estimation is developed. Chapter 6 discusses the efficiency of estimators and some large sample properties, while Chapter 7 studies the topics on confidence intervals. Finally, Chapter 8 is about decision theoretic and Bayesian approach in testing and estimation. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability will highly benefit from this book.
Author : Michael J. Panik
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 21,73 MB
Release : 2012-06-06
Category : Mathematics
ISBN : 1118309804
A concise, easily accessible introduction to descriptive and inferential techniques Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: How do we determine that a given dataset is actually a random sample? With what level of precision and reliability can a population sample be estimated? How are probabilities determined and are they the same thing as odds? How can we predict the level of one variable from that of another? What is the strength of the relationship between two variables? The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material. Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Author : Bernard Flury
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 28,90 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475727658
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.
Author : Prabhanjan N. Tattar
Publisher : John Wiley & Sons
Page : 696 pages
File Size : 47,91 MB
Release : 2016-03-15
Category : Computers
ISBN : 1119152755
Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical concepts Provides graphical presentations inclusive of mathematical expressions Aids understanding of limit theorems of probability with and without the simulation approach Presents detailed algorithmic development of statistical models from scratch Includes practical applications with over 50 data sets
