Simultaneous statistical inference

Rupert G. Miller, Jr

[目次]

  • 1 Introduction.- 1 Case of two means.- 2 Error rates.- 2.1 Probability of a nonzero family error rate.- 2.2 Expected family error rate.- 2.3 Allocation of error.- 3 Basic techniques.- 3.1 Repeated normal statistics.- 3.2 Maximum modulus (Tukey).- 3.3 Bonferroni normal statistics.- 3.4 ?2 projections (Scheffe).- 3.5 Allocation.- 3.6 Multiple modulus tests (Duncan).- 3.7 Least significant difference test (Fisher).- 4 p-mean significance levels.- 5 Families.- 2 Normal Univariate Techniques.- 1 Studentized range (Tukey).- 1.1 Method.- 1.2 Applications.- 1.3 Comparison.- 1.4 Derivation.- 1.5 Distributions and tables.- 2 F projections (Scheffe)48.- 2.1 Method.- 2.2 Applications.- 2.3 Comparison.- 2.4 Derivation.- 2.5 Distributions and tables.- 3 Bonferroni t statistics.- 3.1 Method.- 3.2 Applications.- 3.3 Comparison.- 3.4 Derivation.- 3.5 Distributions and tables.- 4 Studentized maximum modulus.- 4.1 Method.- 4.2 Applications.- 4.3 Comparison.- 4.4 Derivation.- 4.5 Distributions and tables.- 5 Many-one t statistics76.- 5.1 Method.- 5.2 Applications.- 5.3 Comparison.- 5.4 Derivation.- 5.5 Distributions and tables.- 6 Multiple range tests (Duncan).- 6.1 Method.- 6.2 Applications.- 6.3 Comparison.- 6.4 Derivation.- 6.5 Distributions and tables.- 7 Least significant difference test (Fisher).- 7.1 Method.- 7.2 Applications.- 7.3 Comparison.- 7.4 Derivation.- 7.5 Distributions and tables.- 8 Other techniques.- 8.1 Tukey's gap-straggler-variance test.- 8.2 Shortcut methods.- 8.3 Multiple F tests.- 8.4 Two-sample confidence intervals of predetermined length.- 8.5 An improved Bonferroni inequality.- 9 Power.- 10 Robustness.- 3 Regression Techniques.- 1 Regression surface confidence bands.- 1.1 Method.- 1.2 Comparison.- 1.3 Derivation.- 2 Prediction.- 2.1 Method.- 2.2 Comparison.- 2.3 Derivation.- 3 Discrimination.- 3.1 Method.- 3.2 Comparison.- 3.3 Derivation.- 4 Other techniques.- 4.1 Linear confidence bands.- 4.2 Tolerance intervals.- 4.3 Unlimited discrimination intervals.- 4 Nonparametric Techniques.- 1 Many-one sign statistics (Steel).- 1.1 Method.- 1.2 Applications.- 1.3 Comparison.- 1.4 Derivation.- 1.5 Distributions and tables.- 2 k-sample sign statistics.- 2.1 Method.- 2.2 Applications.- 2.3 Comparison.- 2.4 Derivation.- 2.5 Distributions and tables.- 3 Many-one rank statistics (Steel).- 3.1 Method.- 3.2 Applications.- 3.3 Comparison.- 3.4 Derivation.- 3.5 Distributions and tables.- 4 k-sample rank statistics.- 4.1 Method.- 4.2 Applications.- 4.3 Comparison.- 4.4 Derivation.- 4.5 Distributions and tables.- 5 Signed-rank statistics.- 6 Kruskal-Wallis rank statistics (Nemenyi).- 6.1 Method.- 6.2 Applications.- 6.3 Comparison.- 6.4 Derivation.- 6.5 Distributions and tables.- 7 Friedman rank statistics (Nemenyi).- 7.1 Method.- 7.2 Applications.- 7.3 Comparison.- 7.4 Derivation.- 7.5 Distributions and tables.- 8 Other techniques.- 8.1 Permutation tests.- 8.2 Median tests (Nemenyi).- 8.3 Kolmogorov-Smirnov statistics.- 5 Multivariate Techniques.- 1 Single population
  • covariance scalar unknown.- 1.1 Method.- 1.2 Applications.- 1.3 Comparison.- 1.4 Derivation.- 1.5 Distributions and tables.- 2 Single population
  • covariance matrix unknown.- 2.1 Method.- 2.2 Applications.- 2.3 Comparison.- 2.4 Derivation.- 2.5 Distributions and tables.- 3 k populations
  • covariance matrix unknown.- 3.1 Method.- 3.2 Applications.- 3.3 Comparison.- 3.4 Derivation.- 3.5 Distributions and tables.- 4 Other techniques.- 4.1 Variances known
  • covariances unknown.- 4.2 Variance-covariance intervals.- 4.3 Two-sample confidence intervals of predetermined length.- 6 Miscellaneous Techniques.- 1 Outlier detection.- 2 Multinomial populations.- 2.1 Single population.- 2.2 Several populations.- 2.3 Cross-product ratios.- 2.4 Logistic response curves.- 3 Equality of variances.- 4 Periodogram analysis.- 5 Alternative approaches: selection, ranking, slippage.- A Strong Law For The Expected Error Rate.- B TABLES.- I Percentage points of the studentized range.- II Percentage points of the Bonferroni t statistic.- III Percentage points of the studentized maximum modulus.- IV Percentage points of the many-one t statistics.- V Percentage points of the Duncan multiple range test.- VI Percentage points of the many-one sign statistics.- VIII Percentage points of the many-one rank statistics.- IX Percentage points of the k-sample rank statistics.- Developments in Multiple Comparisons 1966-1976.- 1 Introduction.- 2 Papers of special interest.- 2.1 Probability inequalities.- 2.2 Methods for unbalanced ANOVA.- 2.3 Conditional confidence levels.- 2.4 Empirical Bayes approach.- 2.5 Confidence bands in regression.- 3 References.- 4 Bibliography 1966-1976.- 4.1 Survey articles.- 4.2 Probability inequalities.- 4.3 Tables.- 4.4 Normal multifactor methods.- 4.5 Regression.- 4.6 Categorical data.- 4.7 Nonparametric techniques.- 4.8 Multivariate methods.- 4.9 Miscellaneous.- 4.10 Pre-1966 articles missed in [6].- 4.11 Late additions.- 5 List of journals scanned.- Addendum New Table of the Studentized Maximum Modulus.- Table IIIA Percentage points of the studentized maximum modulus.- Author Index.

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この本の情報

書名 Simultaneous statistical inference
著作者等 Miller, Rupert G
Miller Rupert G. Jr.
シリーズ名 Springer series in statistics
出版元 Springer
刊行年月 c1981
版表示 2nd ed
ページ数 xvi, 299 p.
大きさ 25 cm
ISBN 3540905480
0387905480
9781461381242
NCID BA0325037X
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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