M-statistics

Eugene Demidenko is Professor of Biomedical Data Science at the Geisel School of Medicine and Mathematics at Dartmouth. He is a member of the American Statistical Association (ASA) and the Society of Industrial and Applied Mathematics (SIAM). In statistics, Professor Demidenko’s research includes statistical methodology, mixed models, and nonlinear regression. In applied mathematics, he contributed to existence and uniqueness of global minimum, tumor regrowth theory, shape and image analysis, and solving ill-posed problems via mixed boundary partial differential equations. He is the author of two books published by Wiley in 2013 and 2020 “Mixed Models: Theory and Applications” and “Advanced Statistics with Applications in R.” The latter book received a prestigious Ziegel Book Award in Statistics from Technometrics/ASA journal in 2022.

• Preface xi1 Limitations of classic statistics and motivation 11.1 Limitations of classic statistics 21.1.1 Mean 21.1.2 Unbiasedness 41.1.3 Limitations of equal-tail statistical inference 51.2 The rationale for a new statistical theory 51.3 Motivating example: normal variance 71.3.1 Confidence interval for the normal variance 71.3.2 Hypothesis testing for the variance 121.3.3 MC and MO estimators of the variance 141.3.4 Sample size determination for variance 151.4 Neyman-Pearson lemma and its extensions 171.4.1 Introduction 171.4.2 Two lemmas 19References 282 Maximum concentration statistics 312.1 Assumptions 312.2 Short confidence interval and MC estimator 342.3 Density level test 422.4 Efficiency and the sufficient statistic 452.5 Parameter is positive or belongs to a finite interval 482.5.1 Parameter is positive 482.5.2 Parameter belongs to a finite interval 50References 513 Mode statistics 533.1 Unbiased test 533.2 Unbiased CI and MO estimator 583.3 Cumulative information and the sufficient statistic 61References 654 P -value and duality 674.1 P -value for the double-sided hypothesis 674.1.1 General definition 684.1.2 P -value for normal variance 724.2 The overall powerful test 774.3 Duality: converting the CI into a hypothesis test 834.4 Bypassing assumptions 854.5 Overview 86References 895 M-statistics for major statistical parameters 915.1 Exact statistical inference for standard deviation 915.1.1 MC-statistics 925.1.2 MC-statistics on the log scale 945.1.3 MO-statistics 955.1.4 Computation of the p-value 955.2 Pareto distribution 955.2.1 Confidence intervals 965.2.2 Hypothesis testing 995.3 Coefficient of variation for lognormal distribution 1015.4 Statistical testing for two variances 1035.4.1 Computation of the p-value 1055.4.2 Optimal sample size 1065.5 Inference for two-sample exponential distribution 1065.5.1 Unbiased statistical test 1085.5.2 Confidence intervals 1105.5.3 The MC estimator of ν 1125.6 Effect size and coefficient of variation 1135.6.1 Effect size 1145.6.2 Coefficient of variation 1205.6.3 Double-sided hypothesis tests 1255.6.4 Multivariate ES 1265.7 Binomial probability 1275.7.1 The MCL estimator 1285.7.2 The MCL2 estimator 1305.7.3 The MCL2 estimator of pn 1315.7.4 Confidence interval on the double-log scale 1325.7.5 Equal-tail and unbiased tests 1345.8 Poisson rate 1375.8.1 Two-sided short CI on the log scale 1385.8.2 Two-sided tests and p-value 1405.8.3 The MCL estimator of the rate parameter 1425.9 Meta-analysis model 1435.9.1 CI and MCL estimator 1465.10 M-statistics for the correlation coefficient 1495.10.1 MC and MO estimators 1505.10.2 Equal-tail and unbiased tests 1535.10.3 Power function and p-value 1545.10.4 Confidence intervals 1565.11 The square multiple correlation coefficient 1595.11.1 Unbiased statistical test 1605.11.2 Computation of p-value 1635.11.3 Confidence intervals 1645.11.4 The two-sided CI on the log scale 1655.11.5 The MCL estimator 1665.12 Coefficient of determination for linear model 1685.12.1 CoD and multiple correlation coefficient 1695.12.2 Unbiased test 1705.12.3 The MCL estimator for CoD 171References 1736 Multidimensional parameter 1776.1 Density level test 1776.2 Unbiased test 1806.3 Confidence region dual to the DL test 1816.4 Unbiased confidence region 1846.5 Simultaneous inference for normal mean and standard deviation 1876.5.1 Statistical test 1876.5.2 Confidence region 1926.6 Exact confidence inference for parameters of the beta distribution 1946.6.1 Statistical tests 1966.6.2 Confidence regions 1976.7 Two-sample binomial probability 1996.7.1 Hypothesis testing 1996.7.2 Confidence region 2026.8 Exact and profile statistical inference for nonlinear regression 2046.8.1 Statistical inference for the whole parameter 2056.8.2 Statistical inference for an individual parameter of interest via profiling 210References 215Index 219