M-STATISTICS A comprehensive resource providing new statistical methodologies and demonstrating how new approaches work for applications
M-statistics introduces a new approach to statistical inference, redesigning the fundamentals of statistics, and improving on the classical methods we already use. This book targets exact optimal statistical inference for a small sample under one methodological umbrella. Two competing approaches are offered: maximum concentration (MC) and mode (MO) statistics combined under one methodological umbrella, which is why the symbolic equation M=MC+MO. M-statistics defines an estimator as the limit point of the MC or MO exact optimal confidence interval when the confidence level approaches zero, the MC and MO estimator, respectively. Neither mean nor variance plays a role in M-statistics theory.
Novel statistical methodologies in the form of double-sided unbiased and short confidence intervals and tests apply to major statistical parameters:
Exact statistical inference for small sample sizes is illustrated with effect size and coefficient of variation, the rate parameter of the Pareto distribution, two-sample statistical inference for normal variance, and the rate of exponential distributions. M-statistics is illustrated with discrete, binomial, and Poisson distributions. Novel estimators eliminate paradoxes with the classic unbiased estimators when the outcome is zero. Exact optimal statistical inference applies to correlation analysis including Pearson correlation, squared correlation coefficient, and coefficient of determination. New MC and MO estimators along with optimal statistical tests, accompanied by respective power functions, are developed. M-statistics is extended to the multidimensional parameter and illustrated with the simultaneous statistical inference for the mean and standard deviation, shape parameters of the beta distribution, the two-sample binomial distribution, and finally, nonlinear regression. Our new developments are accompanied by respective algorithms and R codes, available at GitHub, and as such readily available for applications.
M-statistics is suitable for professionals and students alike. It is highly useful for theoretical statisticians and teachers, researchers, and data science analysts as an alternative to classical and approximate statistical inference.

lgli/Demidenko E. M-statistics.. optimal statistical inference for a small sample (Wiley, 2023)(ISBN 9781119891796)(O)(387s)_MVsa_.pdf

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M-Statistics: A New Statistical Theory

John Wiley & Sons, Incorporated

American Geophysical Union

Wiley-Blackwell

United States, United States of America

{"isbns":["1119891795","9781119891796"],"last_page":240,"publisher":"Wiley"}

A comprehensive resource providing new statistical methodologies and demonstrating how new approaches work for applications
M-statistics introduces a new approach to statistical inference, redesigning the fundamentals of statistics and improving on the classical methods we already use. This book targets exact optimal statistical inference for a small sample under one methodological umbrella. Two competing approaches are offered: maximum concentration (MC) and mode (MO) statistics combined under one methodological umbrella, which is why the symbolic equation M=MC+MO. M-statistics defines an estimator as the limit point of the MC or MO exact optimal confidence interval when the confidence level approaches zero, the MC and MO estimator, respectively. Neither mean nor variance plays a role in M-statistics theory.
Novel statistical methodologies in the form of double-sided unbiased and short confidence intervals and tests apply to major statistical parameters:
Exact statistical inference for small sample sizes is illustrated with effect size and coefficient of variation, the rate parameter of the Pareto distribution, two-sample statistical inference for normal variance, and the rate of exponential distributions.
M-statistics is illustrated with discrete, binomial and Poisson distributions. Novel estimators eliminate paradoxes with the classic unbiased estimators when the outcome is zero.
Exact optimal statistical inference applies to correlation analysis including Pearson correlation, squared correlation coefficient, and coefficient of determination. New MC and MO estimators along with optimal statistical tests, accompanied by respective power functions, are developed.
M-statistics is extended to the multidimensional parameter and illustrated with the simultaneous statistical inference for the mean and standard deviation, shape parameters of the beta distribution, the two-sample binomial distribution, and finally, nonlinear regression.
The new developments are accompanied by respective algorithms and R codes, available at GitHub, and as such readily available for applications.
M-statistics is suitable for professionals and students alike. It is highly useful for theoretical statisticians and teachers, researchers, and data science analysts as an alternative to classical and approximate statistical inference.

Title Page
Copyright
Dedication
Preface
Chapter 1: Limitations of classic statistics and motivation
1.1 Limitations of classic statistics
1.2 The rationale for a new statistical theory
1.3 Motivating example: normal variance
1.4 Neyman-Pearson lemma and its extensions
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
References
Chapter 3: Mode statistics
3.1 Unbiased test
3.2 Unbiased CI and MO estimator
3.3 Cumulative information and the sufficient statistic
References
Chapter 4: P-value and duality
4.1 P-value for the double-sided hypothesis
4.2 The overall powerful test
4.3 Duality: converting the CI into a hypothesis test
4.4 Bypassing assumptions
4.5 Overview
References
Chapter 5: M-statistics for major statistical parameters
5.1 Exact statistical inference for standard deviation
5.2 Pareto distribution
5.3 Coefficient of variation for lognormal distribution
5.4 Statistical testing for two variances
5.5 Inference for two-sample exponential distribution
5.6 Effect size and coefficient of variation
5.7 Binomial probability
5.8 Poisson rate
5.9 Meta-analysis model
5.10 M-statistics for the correlation coefficient
5.11 The square multiple correlation coefficient
5.12 Coefficient of determination for linear model
References
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
6.6 Exact confidence inference for parameters of the beta distribution
6.7 Two-sample binomial probability
6.8 Exact and profile statistical inference for nonlinear regression
References
Index

"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

2023-10-18