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M-Statistics : Optimal Statistical Inference for a Small Sample
M-Statistics : Optimal Statistical Inference for a Small Sample
Autore Demidenko Eugene
Edizione [1st ed.]
Pubbl/distr/stampa Newark : , : John Wiley & Sons, Incorporated, , 2023
Descrizione fisica 1 online resource (243 pages)
Disciplina 519.5/4
Soggetto topico Mathematical statistics
ISBN 1-119-89182-5
1-119-89180-9
1-119-89181-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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 -- 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 -- 4.1.1 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 -- References -- 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 -- 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 -- 6.5.1 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 -- References -- Index -- EULA.
Record Nr. UNINA-9910830302503321
Demidenko Eugene  
Newark : , : John Wiley & Sons, Incorporated, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
M-Statistics : Optimal Statistical Inference for a Small Sample
M-Statistics : Optimal Statistical Inference for a Small Sample
Autore Demidenko Eugene
Edizione [1st ed.]
Pubbl/distr/stampa Newark : , : John Wiley & Sons, Incorporated, , 2023
Descrizione fisica 1 online resource (243 pages)
Disciplina 519.5/4
Soggetto topico Mathematical statistics
ISBN 1-119-89182-5
1-119-89180-9
1-119-89181-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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 -- 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 -- 4.1.1 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 -- References -- 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 -- 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 -- 6.5.1 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 -- References -- Index -- EULA.
Record Nr. UNINA-9910840711803321
Demidenko Eugene  
Newark : , : John Wiley & Sons, Incorporated, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui