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Record Nr. |
UNINA9910826910103321 |
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Autore |
Pesarin Fortunato |
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Titolo |
Permutation tests for complex data [[electronic resource] ] : theory, applications, and software / / Fortunato Pesarin, Luigi Salmaso |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley, 2010 |
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ISBN |
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1-282-55043-8 |
9786612550430 |
0-470-68951-X |
0-470-68952-8 |
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Descrizione fisica |
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1 online resource (450 p.) |
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Collana |
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Wiley series in probability and statistics |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Statistical hypothesis testing |
Permutations |
Multivariate analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Permutation Tests for Complex Data; Contents; Preface; Notation and Abbreviations; 1 Introduction; 1.1 On Permutation Analysis; 1.2 The Permutation Testing Principle; 1.2.1 Nonparametric Family of Distributions; 1.2.2 The Permutation Testing Principle; 1.3 Permutation Approaches; 1.4 When and Why Conditioning is Appropriate; 1.5 Randomization and Permutation; 1.6 Computational Aspects; 1.7 Basic Notation; 1.8 A Problem with Paired Observations; 1.8.1 Modelling Responses; 1.8.2 Symmetry Induced by Exchangeability; 1.8.3 Further Aspects; 1.8.4 The Student's t-Paired Solution |
1.8.5 The Signed Rank Test Solution1.8.6 The McNemar Solution; 1.9 The Permutation Solution; 1.9.1 General Aspects; 1.9.2 The Permutation Sample Space; 1.9.3 The Conditional Monte Carlo Method; 1.9.4 Approximating the Permutation Distribution; 1.9.5 Problems and Exercises; 1.10 A Two-Sample Problem; 1.10.1 Modelling Responses; 1.10.2 The Student t Solution; 1.10.3 The Permutation Solution; 1.10.4 Rank Solutions; 1.10.5 Problems and Exercises; 1.11 One-Way ANOVA; 1.11.1 Modelling Responses; 1.11.2 Permutation Solutions; 1.11.3 |
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Problems and Exercises |
2 Theory of One-Dimensional Permutation Tests2.1 Introduction; 2.1.1 Notation and Basic Assumptions; 2.1.2 The Conditional Reference Space; 2.1.3 Conditioning on a Set of Sufficient Statistics; 2.2 Definition of Permutation Tests; 2.2.1 General Aspects; 2.2.2 Randomized Permutation Tests; 2.2.3 Non-randomized Permutation Tests; 2.2.4 The p-Value; 2.2.5 A CMC Algorithm for Estimating the p-Value; 2.3 Some Useful Test Statistics; 2.4 Equivalence of Permutation Statistics; 2.4.1 Some Examples; 2.4.2 Problems and Exercises; 2.5 Arguments for Selecting Permutation Tests |
2.6 Examples of One-Sample Problems2.6.1 A Problem with Repeated Observations; 2.6.2 Problems and Exercises; 2.7 Examples of Multi-Sample Problems; 2.8 Analysis of Ordered Categorical Variables; 2.8.1 General Aspects; 2.8.2 A Solution Based on Score Transformations; 2.8.3 Typical Goodness-of-Fit Solutions; 2.8.4 Extension to Non-Dominance Alternatives and C Groups; 2.9 Problems and Exercises; 3 Further Properties of Permutation Tests; 3.1 Unbiasedness of Two-sample Tests; 3.1.1 One-Sided Alternatives; 3.1.2 Two-Sided Alternatives; 3.2 Power Functions of Permutation Tests |
3.2.1 Definition and Algorithm for the Conditional Power3.2.2 The Empirical Conditional ROC Curve; 3.2.3 Definition and Algorithm for the Unconditional Power: Fixed Effects; 3.2.4 Unconditional Power: Random Effects; 3.2.5 Comments on Power Functions; 3.3 Consistency of Permutation Tests; 3.4 Permutation Confidence Interval for d; 3.4.1 Problems and Exercises; 3.5 Extending Inference from Conditional to Unconditional; 3.6 Optimal Properties; 3.6.1 Problems and Exercises; 3.7 Some Asymptotic Properties; 3.7.1 Introduction; 3.7.2 Two Basic Theorems; 3.8 Permutation Central Limit Theorems |
3.8.1 Basic Notions |
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Sommario/riassunto |
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Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today's current thinking. Key Features:Examines the mos |
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