Statistical Inference: Testing Of Hypotheses PDF Download

Author: Srivastava & Srivastava
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812033728X
Category : Reference
Languages : en
Pages : 414

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Book Description
it emphasizes on J. Neyman and Egon Pearson's mathematical foundations of hypothesis testing, which is one of the finest methodologies of reaching conclusions on population parameter. Following Wald and Ferguson's approach, the book presents Neyman-Pearson theory under broader premises of decision theory resulting into simplification and generalization of results. On account of smooth mathematical development of this theory, the book outlines the main result on Lebesgue theory in abstract spaces prior to rigorous theoretical developments on most powerful (MP), uniformly most powerful (UMP) and UMP unbiased tests for different types of testing problems. Likelihood ratio tests their large sample properties to variety of testing situations and connection between confidence estimation and testing of hypothesis have been discussed in separate chapters. The book illustrates simplification of testing problems and reduction in dimensionality of class of tests resulting into existence of an optimal test through the principle of sufficiency and invariance. It concludes with rigorous theoretical developments on non-parametric tests including their optimality, asymptotic relative efficiency, consistency, and asymptotic null distribution.

Author: Prof.Prakash S.Chougule
Publisher: Blue Rose Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 296

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Book Description
The book “Statistical Inference: Testing of Hypothesis” aims to help the student in gaining knowledge about Statistical Inference. This book contains four chapters like Parametric test, Likelihood Ratio Test, Sequential Probability Ratio Test and Non-parametric Tests. Every chapter has been divided into several headings and sub headings to offer clarity and conciseness. The authors have tried his best to simplify units and are written in very simple and lucid language, so that the reader can get an intuitive understanding the contains of the book. The number of examples included in the book will really make the study very easy and yet efficient. Inclusion of question bank and relative exercise, including a lot of multiple choice questions, at the end of each chapter will helps the students to evaluate themselves. The book will particularly help students who are pursuing B.Sc. and M.Sc. in Statistics.

Author: Chester Ismay
Publisher: CRC Press
ISBN: 1000763463
Category : Mathematics
Languages : en
Pages : 461

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Book Description
Statistical Inference via Data Science: A ModernDive into R and the Tidyverse provides a pathway for learning about statistical inference using data science tools widely used in industry, academia, and government. It introduces the tidyverse suite of R packages, including the ggplot2 package for data visualization, and the dplyr package for data wrangling. After equipping readers with just enough of these data science tools to perform effective exploratory data analyses, the book covers traditional introductory statistics topics like confidence intervals, hypothesis testing, and multiple regression modeling, while focusing on visualization throughout. Features: ● Assumes minimal prerequisites, notably, no prior calculus nor coding experience ● Motivates theory using real-world data, including all domestic flights leaving New York City in 2013, the Gapminder project, and the data journalism website, FiveThirtyEight.com ● Centers on simulation-based approaches to statistical inference rather than mathematical formulas ● Uses the infer package for "tidy" and transparent statistical inference to construct confidence intervals and conduct hypothesis tests via the bootstrap and permutation methods ● Provides all code and output embedded directly in the text; also available in the online version at moderndive.com This book is intended for individuals who would like to simultaneously start developing their data science toolbox and start learning about the inferential and modeling tools used in much of modern-day research. The book can be used in methods and data science courses and first courses in statistics, at both the undergraduate and graduate levels.

Author: Deborah G. Mayo
Publisher: Cambridge University Press
ISBN: 1108563309
Category : Mathematics
Languages : en
Pages : 503

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Book Description
Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.

Author: Erich Leo Lehmann
Publisher: Springer Verlag
ISBN: 0387949194
Category : Mathematics
Languages : en
Pages : 600

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Book Description
This classic work, now available from Springer, summarizes developments in the field of hypotheses testing. Optimality considerations continue to provide the organizing principle; however, they are now tempered by a much stronger emphasis on the robustness properties of the resulting procedures. This book is an essential reference for any graduate student in statistics.

Author: M. RAJAGOPALAN
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120346351
Category : Mathematics
Languages : en
Pages : 408

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Book Description
Intended as a text for the postgraduate students of statistics, this well-written book gives a complete coverage of Estimation theory and Hypothesis testing, in an easy-to-understand style. It is the outcome of the authors’ teaching experience over the years. The text discusses absolutely continuous distributions and random sample which are the basic concepts on which Statistical Inference is built up, with examples that give a clear idea as to what a random sample is and how to draw one such sample from a distribution in real-life situations. It also discusses maximum-likelihood method of estimation, Neyman’s shortest confidence interval, classical and Bayesian approach. The difference between statistical inference and statistical decision theory is explained with plenty of illustrations that help students obtain the necessary results from the theory of probability and distributions, used in inference.

Author: Gregory J. Privitera
Publisher: SAGE
ISBN: 141296931X
Category : Mathematics
Languages : en
Pages : 737

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Book Description
Statistics for the Behavioral Sciences is an introduction to statistics text that will engage students in an ongoing spirit of discovery by illustrating how statistics apply to modern-day research problems. By integrating instructions, screenshots, and practical examples for using IBM SPSS® Statistics software, the book makes it easy for students to learn statistical concepts within each chapter. Gregory J. Privitera takes a user-friendly approach while balancing statistical theory, computation, and application with the technical instruction needed for students to succeed in the modern era of data collection, analysis, and statistical interpretation.

Author: S.D. Silvey
Publisher: Routledge
ISBN: 1351414496
Category : Mathematics
Languages : en
Pages : 157

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Book Description
Statistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions

Author: MANOJ KUMAR SRIVASTAVA
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812034930X
Category : Mathematics
Languages : en
Pages : 808

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Book Description
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.

Author: Vijay K. Rohatgi
Publisher: Courier Corporation
ISBN: 0486136213
Category : Mathematics
Languages : en
Pages : 956

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Book Description
This treatment of probability and statistics examines discrete and continuous models, functions of random variables and random vectors, large-sample theory, more. Hundreds of problems (some with solutions). 1984 edition. Includes 144 figures and 35 tables.