A First Course In Statistical Inference

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First Course In Statistical Inference

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Author : Jonathan Gillard
language : en
Publisher:
Release Date : 2020

First Course In Statistical Inference written by Jonathan Gillard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Inference categories.

This book offers a modern and accessible introduction to Statistical Inference, the science of inferring key information from data. Aimed at beginning undergraduate students in mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a conversational and informal style, this concise text concentrates on ideas and concepts, with key theorems stated and proved. Detailed worked examples are included and each chapter ends with a set of exercises, with full solutions given at the back of the book. Examples using R are provided throughout the book, with a brief guide to the software included. Topics covered in the book include: sampling distributions, properties of estimators, confidence intervals, hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author's extensive teaching experience, the material of the book has been honed by student feedback for over a decade. Assuming only some familiarity with elementary probability, this textbook has been devised for a one semester first course in statistics.

A First Course In Probability Models And Statistical Inference

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Author : James H.C. Creighton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A First Course In Probability Models And Statistical Inference written by James H.C. Creighton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Welcome to new territory: A course in probability models and statistical inference. The concept of probability is not new to you of course. You've encountered it since childhood in games of chance-card games, for example, or games with dice or coins. And you know about the "90% chance of rain" from weather reports. But once you get beyond simple expressions of probability into more subtle analysis, it's new territory. And very foreign territory it is. You must have encountered reports of statistical results in voter sur veys, opinion polls, and other such studies, but how are conclusions from those studies obtained? How can you interview just a few voters the day before an election and still determine fairly closely how HUN DREDS of THOUSANDS of voters will vote? That's statistics. You'll find it very interesting during this first course to see how a properly designed statistical study can achieve so much knowledge from such drastically incomplete information. It really is possible-statistics works! But HOW does it work? By the end of this course you'll have understood that and much more. Welcome to the enchanted forest.

A First Course In Multivariate Statistics

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Author : Bernhard Flury
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-15

A First Course In Multivariate Statistics written by Bernhard Flury and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-15 with Mathematics categories.

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 Inference

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Author : George Casella
language : en
Publisher: CRC Press
Release Date : 2024-05-23

Statistical Inference written by George Casella and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-23 with Mathematics categories.

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

A First Course In Statistics

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Author : James T. McClave
language : en
Publisher: Weidenfeld & Nicolson
Release Date : 1989

A First Course In Statistics written by James T. McClave and has been published by Weidenfeld & Nicolson this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

All Of Nonparametric Statistics

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Author : Larry Wasserman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10

All Of Nonparametric Statistics written by Larry Wasserman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-10 with Mathematics categories.

There are many books on various aspects of nonparametric inference such as density estimation, nonparametric regression, bootstrapping, and wavelets methods. But it is hard to ?nd all these topics covered in one place. The goal of this text is to provide readers with a single book where they can ?nd a brief account of many of the modern topics in nonparametric inference. The book is aimed at master’s-level or Ph. D. -level statistics and computer science students. It is also suitable for researchersin statistics, machine lea- ing and data mining who want to get up to speed quickly on modern n- parametric methods. My goal is to quickly acquaint the reader with the basic concepts in many areas rather than tackling any one topic in great detail. In the interest of covering a wide range of topics, while keeping the book short, I have opted to omit most proofs. Bibliographic remarks point the reader to references that contain further details. Of course, I have had to choose topics to include andto omit,the title notwithstanding. For the mostpart,I decided to omit topics that are too big to cover in one chapter. For example, I do not cover classi?cation or nonparametric Bayesian inference. The book developed from my lecture notes for a half-semester (20 hours) course populated mainly by master’s-level students. For Ph. D.

Measure Theory And Probability Theory

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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-27

Measure Theory And Probability Theory written by Krishna B. Athreya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-27 with Business & Economics categories.

This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute.

Basic Principles Of Structural Equation Modeling

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Author : Ralph O. Mueller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Basic Principles Of Structural Equation Modeling written by Ralph O. Mueller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.

During the last two decades, structural equation modeling (SEM) has emerged as a powerful multivariate data analysis tool in social science research settings, especially in the fields of sociology, psychology, and education. Although its roots can be traced back to the first half of this century, when Spearman (1904) developed factor analysis and Wright (1934) introduced path analysis, it was not until the 1970s that the works by Karl Joreskog and his associates (e. g. , Joreskog, 1977; Joreskog and Van Thillo, 1973) began to make general SEM techniques accessible to the social and behavioral science research communities. Today, with the development and increasing avail ability of SEM computer programs, SEM has become a well-established and respected data analysis method, incorporating many of the traditional analysis techniques as special cases. State-of-the-art SEM software packages such as LISREL (Joreskog and Sorbom, 1993a,b) and EQS (Bentler, 1993; Bentler and Wu, 1993) handle a variety of ordinary least squares regression designs as well as complex structural equation models involving variables with arbitrary distributions. Unfortunately, many students and researchers hesitate to use SEM methods, perhaps due to the somewhat complex underlying statistical repre sentation and theory. In my opinion, social science students and researchers can benefit greatly from acquiring knowledge and skills in SEM since the methods-applied appropriately-can provide a bridge between the theo retical and empirical aspects of behavioral research.

Statistical Analysis And Data Display

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Author : Richard M. Heiberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Statistical Analysis And Data Display written by Richard M. Heiberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

1 Audience Students seeking master's degrees in applied statistics in the late 1960s and 1970s typically took a year-long sequence in statistical methods. Popular choices of the course text book in that period prior to the availability of high speed computing and graphics capability were those authored by Snedecor and Cochran, and Steel and Torrie. By 1980, the topical coverage in these classics failed to include a great many new and important elementary techniques in the data analyst's toolkit. In order to teach the statistical methods sequence with adequate coverage of topics, it became necessary to draw material from each of four or five text sources. Obviously, such a situation makes life difficult for both students and instructors. In addition, statistics students need to become proficient with at least one high-quality statistical software package. This book can serve as a standalone text for a contemporary year-long course in statistical methods at a level appropriate for statistics majors at the master's level or other quantitatively oriented disciplines at the doctoral level. The topics include both concepts and techniques developed many years ago and a variety of newer tools not commonly found in textbooks.

Probability Via Expectation

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Author : Peter Whittle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Probability Via Expectation written by Peter Whittle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The third edition of 1992 constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write. The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations. These are substantial topics, but ones into which one can gain an insight with less labour than is generally thought. They all involve the expectation concept in an essential fashion, even the treatment of option pricing, which seems initially to forswear expectation in favour of an arbitrage criterion. I am grateful to readers and to Springer-Verlag for their continuing interest in the approach taken in this work. Peter Whittle Preface to the Third Edition This book is a complete revision of the earlier work Probability which appeared in 1970. While revised so radically and incorporatingso much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, demanding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level' . In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character.