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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 book 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.

# ISBN 9781118387986

## Mixed Models: Theory and Applications with R Second Edition

This book features unique applications of mixed model methodology, as well as:

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• Comprehensive theoretical discussions illustrated by examples and figures

• Problems and extended projects requiring simulations in R intended to reinforce material

• Summaries of major results and general points of discussion at the end of each chapter

• Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations

• Over 300 exercises, end-of-section problems, updated data sets, and R subroutines

ISBN 9781118091579

PROFESSOR EUGENE DEMIDENKO works at Dartmouth College in the Department of Biomedical Science, he teaches statistics at Mathematics Department to undergraduate students and to graduate students at Quantitative Biomedical Sciences at Geisel School of Medicine. He has brought experience in theoretical and applied statistics, such as epidemiology and biostatistics, statistical analysis of images, tumor regrowth, ill-posed inverse problems in engineering and technology, optimal portfolio allocation, among others. His first book with Wiley Mixed Model: Theory and Applications with R gained much popularity among researchers and graduate/PhD students. Prof. Demidenko is the author of a controversial paper The P-value You Can't Buy published in 2016 in The American Statistician.

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According to a recent database compiled by Stanford University, Dr. Demidenko belongs to top 2% World scientists around the globe across all disciplines.