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M-statistics

Optimal Statistical Inference for a Small Sample de

Éditeur :

Wiley


Paru le : 2023-08-01

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Description
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.
Pages
240 pages
Collection
n.c
Parution
2023-08-01
Marque
Wiley
EAN papier
9781119891796
EAN PDF
9781119891802
Informations sur l'ebook
Nombre pages copiables
0
Nombre pages imprimables
240
Taille du fichier
3758 Ko
Prix
117,32 €
EAN EPUB
9781119891819
Informations sur l'ebook
Nombre pages copiables
0
Nombre pages imprimables
240
Taille du fichier
17265 Ko
Prix
117,32 €

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