M-Statistics : Optimal Statistical Inference for a Small Sample.

Format:

Book

Author/Creator:

Demidenko, Eugene.

Language:

English

Subjects (All):

Mathematical statistics.

Physical Description:

1 online resource (243 pages)

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2023.

Summary:

"M-statistics: A New Statistical Perspective introduces a new approach for statistical interference, redesigning the fundamentals of statistics and improving on the classical methods we already use. The author discusses the development of new criteria for efficient estimation and delves into how two methods for statistical intereference are combined under one umbrella to create 'M statistics.' This book develops novel confidence intervals and statistical tests for statistical parameters including effect size, binomial probability, and Poisson rate, ensuring unbiased tests are developed alongside this. Suitable for professionals and students alike, this theoretical book explains how new approaches work for statistical applications and is accompanied with a GitHub repository hosting the R code for every new methodology presented."-- Provided by publisher.

Contents:

Cover

Title Page

Copyright

Contents

Preface

Chapter 1 Limitations of classic statistics and motivation

1.1 Limitations of classic statistics

1.1.1 Mean

1.1.2 Unbiasedness

1.1.3 Limitations of equal‐tail statistical inference

1.2 The rationale for a new statistical theory

1.3 Motivating example: normal variance

1.3.1 Confidence interval for the normal variance

1.3.2 Hypothesis testing for the variance

1.3.3 MC and MO estimators of the variance

1.3.4 Sample size determination for variance

1.4 Neyman‐Pearson lemma and its extensions

1.4.1 Introduction

1.4.2 Two lemmas

References

Chapter 2 Maximum concentration statistics

2.1 Assumptions

2.2 Short confidence interval and MC estimator

2.3 Density level test

2.4 Efficiency and the sufficient statistic

2.5 Parameter is positive or belongs to a finite interval

2.5.1 Parameter is positive

2.5.2 Parameter belongs to a finite interval

Chapter 3 Mode statistics

3.1 Unbiased test

3.2 Unbiased CI and MO estimator

3.3 Cumulative information and the sufficient statistic

Chapter 4 P‐value and duality

4.1 P‐value for the double‐sided hypothesis

4.1.1 General definition

4.1.2 P‐value for normal variance

4.2 The overall powerful test

4.3 Duality: converting the CI into a hypothesis test

4.4 Bypassing assumptions

4.5 Overview

Chapter 5 M‐statistics for major statistical parameters

5.1 Exact statistical inference for standard deviation

5.1.1 MC‐statistics

5.1.2 MC‐statistics on the log scale

5.1.3 MO‐statistics

5.1.4 Computation of the p‐value

5.2 Pareto distribution

5.2.1 Confidence intervals

5.2.2 Hypothesis testing

5.3 Coefficient of variation for lognormal distribution

5.4 Statistical testing for two variances.

5.4.1 Computation of the p‐value

5.4.2 Optimal sample size

5.5 Inference for two‐sample exponential distribution

5.5.1 Unbiased statistical test

5.5.2 Confidence intervals

5.5.3 The MC estimator of ν

5.6 Effect size and coefficient of variation

5.6.1 Effect size

5.6.2 Coefficient of variation

5.6.3 Double‐sided hypothesis tests

5.6.4 Multivariate ES

5.7 Binomial probability

5.7.1 The MCL estimator

5.7.2 The MCL2 estimator

5.7.3 The MCL2 estimator of pn

5.7.4 Confidence interval on the double‐log scale

5.7.5 Equal‐tail and unbiased tests

5.8 Poisson rate

5.8.1 Two‐sided short CI on the log scale

5.8.2 Two‐sided tests and p‐value

5.8.3 The MCL estimator of the rate parameter

5.9 Meta‐analysis model

5.9.1 CI and MCL estimator

5.10 M‐statistics for the correlation coefficient

5.10.1 MC and MO estimators

5.10.2 Equal‐tail and unbiased tests

5.10.3 Power function and p‐value

5.10.4 Confidence intervals

5.11 The square multiple correlation coefficient

5.11.1 Unbiased statistical test

5.11.2 Computation of p‐value

5.11.3 Confidence intervals

5.11.4 The two‐sided CI on the log scale

5.11.5 The MCL estimator

5.12 Coefficient of determination for linear model

5.12.1 CoD and multiple correlation coefficient

5.12.2 Unbiased test

5.12.3 The MCL estimator for CoD

Chapter 6 Multidimensional parameter

6.1 Density level test

6.2 Unbiased test

6.3 Confidence region dual to the DL test

6.4 Unbiased confidence region

6.5 Simultaneous inference for normal mean and standard deviation

6.5.1 Statistical test

6.5.2 Confidence region

6.6 Exact confidence inference for parameters of the beta distribution

6.6.1 Statistical tests

6.6.2 Confidence regions

6.7 Two‐sample binomial probability

6.7.1 Hypothesis testing.

6.7.2 Confidence region

6.8 Exact and profile statistical inference for nonlinear regression

6.8.1 Statistical inference for the whole parameter

6.8.2 Statistical inference for an individual parameter of interest via profiling

Index

EULA.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9781119891826

1119891825

9781119891802

1119891809

9781119891819

1119891817

OCLC:

1375661421