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Record Nr. |
UNINA9910830171303321 |
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Autore |
Staudte Robert G |
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Titolo |
Robust estimation and testing [[electronic resource] /] / Robert G. Staudte, Simon J. Sheather |
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Pubbl/distr/stampa |
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ISBN |
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1-283-27998-3 |
9786613279989 |
1-118-16548-9 |
1-118-16549-7 |
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Descrizione fisica |
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1 online resource (382 p.) |
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Collana |
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Wiley series in probability and mathematical statistics. Applied probability and statistics |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Estimation theory |
Robust statistics |
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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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"A Wiley-Interscience publication." |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Robust Estimation and Testing; Contents; 1. The Field of Statistics; 1.1 The Role of Statistics in Scientific Inference; 1.1.1 The Scientific Method; 1.1.2 Statistical Support for the Scientific Method; 1.1.3 The Significance of a Result; 1.1.4 The Challenge to Statisticians; 1.2 Recent Trends in Statistics; 1.2.1 Mathematical Statistics; 1.2.2 The Impact of Computers; 1.2.3 Robust Statistics; 1.3 The Case for Descriptive Measures; 1.3.1 Nonparametric Neighborhoods of Parametric Models; 1.3.2 Descriptive Measures; 1.4 The Domain and Range of This Book; 1.5 Problems; 1.6 Complements |
1.6.1 Other Approaches to Robust Statistics1.6.2 Significance of an Experimental Result; 2. Estimating Scale-Finite Sample Results; 2.1 Examples; 2.2 Scale Parameter Families; 2.2.1 Definitions and Properties; 2.2.2 Examples of Continuous Scale Parameter Families; 2.3 Finite Sample Properties of Estimators; 2.3.1 Unbiasedness, Scale Equivariance, and Mean Squared Error; 2.3.2 Estimators of an Exponential Scale Parameter; 2.3.3 Mixture Models for Contamination; |
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2.3.4 Simulation Results; 2.3.5 Finite Sample Breakdown Point; 2.4 Standard Errors, the Bootstrap |
2.4.1 Traditional Estimates of Standard Error2.4.2 Bootstrap Estimates of Standard Error; 2.4.3 An Illustration of Bootstrap Calculations; 2.4.4 Evaluating the Standard Error Estimates; 2.5 Problems; 2.6 Complements; 2.6.1 The Breakdown Point; 2.6.2 Further Developments on the Bootstrap; 3. Estimating Scale-Asymptotic Results; 3.1 Consistency, Asymptotic Normality, and Efficiency; 3.1.1 Representing Estimators by Descriptive Measures; 3.1.2 Consistency, Asymptotic Normality, and Relative Efficiency; 3.2 Robustness Concepts; 3.2.1 The Breakdown Point; 3.2.2 The Influence Function |
3.2.3* L-Estimators3.2.4* Qualitative Robustness; 3.2.5 Concluding Remarks; 3.3 Descriptive Measures of Scale; 3.3.1 Measures of Scale; 3.3.2 Efficiency in Terms of Standardized Variance; 3.3.3 Simulation Results; 3.3.4 Summary; 3.4* Stability of Estimators on Neighborhoods of the Exponential Scale Parameter Family; 3.4.1 The Relative Efficiency Approach; 3.4.2 The Infinitesimal Approach; 3.5 Estimates of Standard Error; 3.5.1 Influence Function Estimates; 3.5.2 Bootstrap Estimates of Standard Error; 3.6 Problems; 3.7 Complements; 3.7.1 Sensitivity Curve |
3.7.2 Resistant Estimates and Qualitative Robustness3.7.3 Standard and Nonstandard Errors; 4. Location-Dispersion Estimation; 4.1 Introduction and Examples; 4.1.1 Some Initial Questions; 4.1.2 Examples; 4.2 Location-Scale Parameter Families; 4.2.1 Definitions and Properties; 4.2.2 Examples of Location-Scale Families; 4.3 Estimators of Location; 4.3.1 Descriptive Measures of Location; 4.3.2 L-Estimators; 4.3.3 M-Estimators; 4.3.4 R-Estimators; 4.4 Estimators of Dispersion; 4.4.1 Descriptive Measures of Dispersion; 4.4.2 Performance of Some Dispersion Estimators |
4.5 Joint Estimation of Location and Dispersion |
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Sommario/riassunto |
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An introduction to the theory and methods of robust statistics, providing students with practical methods for carrying out robust procedures in a variety of statistical contexts and explaining the advantages of these procedures. In addition, the text develops techniques and concepts likely to be useful in the future analysis of new statistical models and procedures. Emphasizing the concepts of breakdown point and influence functon of an estimator, it demonstrates the technique of expressing an estimator as a descriptive measure from which its influence function can be derived and then used to |
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