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Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.]
| Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.] |
| Pubbl/distr/stampa | New York, : Wiley, 1986 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina |
519.5
519.54 |
| Altri autori (Persone) | HampelFrank R. <1941-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Robust statistics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-33237-X
9786613332370 1-118-18643-5 1-118-15068-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Robust Statistics: The Approach Based on Influence Functions; Contents; 1. INTRODUCTION AND MOTIVATION; 1.1. The Place and Aims of Robust Statistics; 1.1a. What Is Robust Statistics?; 1.1b. The Relation to Some Other Key Words in Statistics; 1.1c. The Aims of Robust Statistics; 1.1d. An Example; 1.2. Why Robust Statistics?; 1.2a. The Role of Parametric Models; 1.2b. Types of Deviations from Parametric Models; 1.2c. The Frequency of Gross Errors; 1.2d. The Effects of Mild Deviations from a Parametric Model; 1.2e. How Necessary Are Robust Procedures?
1.3. The Main Approaches towards a Theory of Robustness1.3a. Some Historical Notes; 1.3b. Huber's Minimax Approach for Robust Estimation; 1.3c. Huber's Second Approach to Robust Statistics via Robustifed Likelihood Ratio Tests; 1.3d. The Approach Based on In Juence Functions; 1.3e. The Relation between the Minimax Approach and the Approach Based on Influence Functions; 1.3f. The Approach Based on Influence Functions as a Robustifed Likelihood Approach, and Its Relation to Various Statistical Schools; *1.4. Rejection of Outliers and Robust Statistics; 1.4a. Why Rejection of Outliers? 1.4b. How Well Are Objective and Subjective Methods for the Rejection of Outliers Doing in the Context of Robust Estimation?Exercises and Problems; 2. ONE-DIMENSIONAL ESTIMATORS; 2.0. An Introductory Example; 2.1. The Influence Function; 2.1a. Parametric Models, Estimators, and Functionals; 2.1b. Definition and Properties of the Influence Function; 2.1c. Robustness Measures Derived from the Influence Function; 2.1d. Some Simple Examples; 2.1e. Finite-Sample Versions; 2.2. The Breakdown Point and Qualitative Robustness; 2.2a. Global Reliability: The Breakdown Point 2.2b. Continuity and Qualitative Robustness2.3. Classes of Estimators; 2.3a. M-Estimators; 2.3b. L-Estimators; 2.3c. R-Estimators; 2.3d. Other Types of Estimators: A, D, P, S, W; 2.4. Optimally Bounding the Gross-Error Sensitivity; 2.4a. The General Optimality Result; 2.4b. M-Estimator; 2.4c. L-Estimators; 2.4d. R-Estimators; 2.5. The Change-of-Variance Function; 2.5a. Definitions; 2.5b. B-Robustness versus V-Robustness; 2.5c. The Most Robust Estimator; 2.5d. Optimal Robust Estimators; 2.5e. M-Estimators for Scale; *2.5f. Further Topics; 2.6. Redescending M-Estimators; 2.6a. Introduction 2.6b. Most Robust Estimators2.6c. Optimal Robust Estimators; 2.6d. Schematic Summary of Sections 2.5 and 2.6; *2.6e. Redescending M-Estimators for Scale; 2.7. Relation with Huber's Minimax Approach; Exercises and Problems; 3. ONE-DIMENSIONAL TESTS; 3.1. Introduction; 3.2. The Influence Function for Tests; 3.2a. Definition of the Influence Function; 3.2b. Properties of the Influence Function; 3.2c. Relation with Level and Power; 3.2d. Connection with Shift Estimators; 3.3. Classes of Tests; 3.3a The One-Sample Case; 3.3b. The Two-Sample Case; 3.4. Optimally Bounding the Gross-Error Sensitivity 3.5. Extending the Change-of-Variance Function to Tests |
| Record Nr. | UNINA-9910139564803321 |
| New York, : Wiley, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.]
| Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.] |
| Pubbl/distr/stampa | New York, : Wiley, 1986 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina |
519.5
519.54 |
| Altri autori (Persone) | HampelFrank R. <1941-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Robust statistics |
| ISBN |
1-283-33237-X
9786613332370 1-118-18643-5 1-118-15068-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Robust Statistics: The Approach Based on Influence Functions; Contents; 1. INTRODUCTION AND MOTIVATION; 1.1. The Place and Aims of Robust Statistics; 1.1a. What Is Robust Statistics?; 1.1b. The Relation to Some Other Key Words in Statistics; 1.1c. The Aims of Robust Statistics; 1.1d. An Example; 1.2. Why Robust Statistics?; 1.2a. The Role of Parametric Models; 1.2b. Types of Deviations from Parametric Models; 1.2c. The Frequency of Gross Errors; 1.2d. The Effects of Mild Deviations from a Parametric Model; 1.2e. How Necessary Are Robust Procedures?
1.3. The Main Approaches towards a Theory of Robustness1.3a. Some Historical Notes; 1.3b. Huber's Minimax Approach for Robust Estimation; 1.3c. Huber's Second Approach to Robust Statistics via Robustifed Likelihood Ratio Tests; 1.3d. The Approach Based on In Juence Functions; 1.3e. The Relation between the Minimax Approach and the Approach Based on Influence Functions; 1.3f. The Approach Based on Influence Functions as a Robustifed Likelihood Approach, and Its Relation to Various Statistical Schools; *1.4. Rejection of Outliers and Robust Statistics; 1.4a. Why Rejection of Outliers? 1.4b. How Well Are Objective and Subjective Methods for the Rejection of Outliers Doing in the Context of Robust Estimation?Exercises and Problems; 2. ONE-DIMENSIONAL ESTIMATORS; 2.0. An Introductory Example; 2.1. The Influence Function; 2.1a. Parametric Models, Estimators, and Functionals; 2.1b. Definition and Properties of the Influence Function; 2.1c. Robustness Measures Derived from the Influence Function; 2.1d. Some Simple Examples; 2.1e. Finite-Sample Versions; 2.2. The Breakdown Point and Qualitative Robustness; 2.2a. Global Reliability: The Breakdown Point 2.2b. Continuity and Qualitative Robustness2.3. Classes of Estimators; 2.3a. M-Estimators; 2.3b. L-Estimators; 2.3c. R-Estimators; 2.3d. Other Types of Estimators: A, D, P, S, W; 2.4. Optimally Bounding the Gross-Error Sensitivity; 2.4a. The General Optimality Result; 2.4b. M-Estimator; 2.4c. L-Estimators; 2.4d. R-Estimators; 2.5. The Change-of-Variance Function; 2.5a. Definitions; 2.5b. B-Robustness versus V-Robustness; 2.5c. The Most Robust Estimator; 2.5d. Optimal Robust Estimators; 2.5e. M-Estimators for Scale; *2.5f. Further Topics; 2.6. Redescending M-Estimators; 2.6a. Introduction 2.6b. Most Robust Estimators2.6c. Optimal Robust Estimators; 2.6d. Schematic Summary of Sections 2.5 and 2.6; *2.6e. Redescending M-Estimators for Scale; 2.7. Relation with Huber's Minimax Approach; Exercises and Problems; 3. ONE-DIMENSIONAL TESTS; 3.1. Introduction; 3.2. The Influence Function for Tests; 3.2a. Definition of the Influence Function; 3.2b. Properties of the Influence Function; 3.2c. Relation with Level and Power; 3.2d. Connection with Shift Estimators; 3.3. Classes of Tests; 3.3a The One-Sample Case; 3.3b. The Two-Sample Case; 3.4. Optimally Bounding the Gross-Error Sensitivity 3.5. Extending the Change-of-Variance Function to Tests |
| Record Nr. | UNINA-9910643772503321 |
| New York, : Wiley, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.]
| Robust statistics [[electronic resource] ] : the approach based on influence functions / / Frank R. Hampel ... [et al.] |
| Pubbl/distr/stampa | New York, : Wiley, 1986 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina |
519.5
519.54 |
| Altri autori (Persone) | HampelFrank R. <1941-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Robust statistics |
| ISBN |
1-283-33237-X
9786613332370 1-118-18643-5 1-118-15068-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Robust Statistics: The Approach Based on Influence Functions; Contents; 1. INTRODUCTION AND MOTIVATION; 1.1. The Place and Aims of Robust Statistics; 1.1a. What Is Robust Statistics?; 1.1b. The Relation to Some Other Key Words in Statistics; 1.1c. The Aims of Robust Statistics; 1.1d. An Example; 1.2. Why Robust Statistics?; 1.2a. The Role of Parametric Models; 1.2b. Types of Deviations from Parametric Models; 1.2c. The Frequency of Gross Errors; 1.2d. The Effects of Mild Deviations from a Parametric Model; 1.2e. How Necessary Are Robust Procedures?
1.3. The Main Approaches towards a Theory of Robustness1.3a. Some Historical Notes; 1.3b. Huber's Minimax Approach for Robust Estimation; 1.3c. Huber's Second Approach to Robust Statistics via Robustifed Likelihood Ratio Tests; 1.3d. The Approach Based on In Juence Functions; 1.3e. The Relation between the Minimax Approach and the Approach Based on Influence Functions; 1.3f. The Approach Based on Influence Functions as a Robustifed Likelihood Approach, and Its Relation to Various Statistical Schools; *1.4. Rejection of Outliers and Robust Statistics; 1.4a. Why Rejection of Outliers? 1.4b. How Well Are Objective and Subjective Methods for the Rejection of Outliers Doing in the Context of Robust Estimation?Exercises and Problems; 2. ONE-DIMENSIONAL ESTIMATORS; 2.0. An Introductory Example; 2.1. The Influence Function; 2.1a. Parametric Models, Estimators, and Functionals; 2.1b. Definition and Properties of the Influence Function; 2.1c. Robustness Measures Derived from the Influence Function; 2.1d. Some Simple Examples; 2.1e. Finite-Sample Versions; 2.2. The Breakdown Point and Qualitative Robustness; 2.2a. Global Reliability: The Breakdown Point 2.2b. Continuity and Qualitative Robustness2.3. Classes of Estimators; 2.3a. M-Estimators; 2.3b. L-Estimators; 2.3c. R-Estimators; 2.3d. Other Types of Estimators: A, D, P, S, W; 2.4. Optimally Bounding the Gross-Error Sensitivity; 2.4a. The General Optimality Result; 2.4b. M-Estimator; 2.4c. L-Estimators; 2.4d. R-Estimators; 2.5. The Change-of-Variance Function; 2.5a. Definitions; 2.5b. B-Robustness versus V-Robustness; 2.5c. The Most Robust Estimator; 2.5d. Optimal Robust Estimators; 2.5e. M-Estimators for Scale; *2.5f. Further Topics; 2.6. Redescending M-Estimators; 2.6a. Introduction 2.6b. Most Robust Estimators2.6c. Optimal Robust Estimators; 2.6d. Schematic Summary of Sections 2.5 and 2.6; *2.6e. Redescending M-Estimators for Scale; 2.7. Relation with Huber's Minimax Approach; Exercises and Problems; 3. ONE-DIMENSIONAL TESTS; 3.1. Introduction; 3.2. The Influence Function for Tests; 3.2a. Definition of the Influence Function; 3.2b. Properties of the Influence Function; 3.2c. Relation with Level and Power; 3.2d. Connection with Shift Estimators; 3.3. Classes of Tests; 3.3a The One-Sample Case; 3.3b. The Two-Sample Case; 3.4. Optimally Bounding the Gross-Error Sensitivity 3.5. Extending the Change-of-Variance Function to Tests |
| Record Nr. | UNINA-9910830550003321 |
| New York, : Wiley, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Robust statistics : the approach based on influence functions / / Frank R. Hampel ... [et al.]
| Robust statistics : the approach based on influence functions / / Frank R. Hampel ... [et al.] |
| Pubbl/distr/stampa | New York, : Wiley, 1986 |
| Descrizione fisica | 1 online resource (538 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | HampelFrank R. <1941-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Robust statistics |
| ISBN |
1-283-33237-X
9786613332370 1-118-18643-5 1-118-15068-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Robust Statistics: The Approach Based on Influence Functions; Contents; 1. INTRODUCTION AND MOTIVATION; 1.1. The Place and Aims of Robust Statistics; 1.1a. What Is Robust Statistics?; 1.1b. The Relation to Some Other Key Words in Statistics; 1.1c. The Aims of Robust Statistics; 1.1d. An Example; 1.2. Why Robust Statistics?; 1.2a. The Role of Parametric Models; 1.2b. Types of Deviations from Parametric Models; 1.2c. The Frequency of Gross Errors; 1.2d. The Effects of Mild Deviations from a Parametric Model; 1.2e. How Necessary Are Robust Procedures?
1.3. The Main Approaches towards a Theory of Robustness1.3a. Some Historical Notes; 1.3b. Huber's Minimax Approach for Robust Estimation; 1.3c. Huber's Second Approach to Robust Statistics via Robustifed Likelihood Ratio Tests; 1.3d. The Approach Based on In Juence Functions; 1.3e. The Relation between the Minimax Approach and the Approach Based on Influence Functions; 1.3f. The Approach Based on Influence Functions as a Robustifed Likelihood Approach, and Its Relation to Various Statistical Schools; *1.4. Rejection of Outliers and Robust Statistics; 1.4a. Why Rejection of Outliers? 1.4b. How Well Are Objective and Subjective Methods for the Rejection of Outliers Doing in the Context of Robust Estimation?Exercises and Problems; 2. ONE-DIMENSIONAL ESTIMATORS; 2.0. An Introductory Example; 2.1. The Influence Function; 2.1a. Parametric Models, Estimators, and Functionals; 2.1b. Definition and Properties of the Influence Function; 2.1c. Robustness Measures Derived from the Influence Function; 2.1d. Some Simple Examples; 2.1e. Finite-Sample Versions; 2.2. The Breakdown Point and Qualitative Robustness; 2.2a. Global Reliability: The Breakdown Point 2.2b. Continuity and Qualitative Robustness2.3. Classes of Estimators; 2.3a. M-Estimators; 2.3b. L-Estimators; 2.3c. R-Estimators; 2.3d. Other Types of Estimators: A, D, P, S, W; 2.4. Optimally Bounding the Gross-Error Sensitivity; 2.4a. The General Optimality Result; 2.4b. M-Estimator; 2.4c. L-Estimators; 2.4d. R-Estimators; 2.5. The Change-of-Variance Function; 2.5a. Definitions; 2.5b. B-Robustness versus V-Robustness; 2.5c. The Most Robust Estimator; 2.5d. Optimal Robust Estimators; 2.5e. M-Estimators for Scale; *2.5f. Further Topics; 2.6. Redescending M-Estimators; 2.6a. Introduction 2.6b. Most Robust Estimators2.6c. Optimal Robust Estimators; 2.6d. Schematic Summary of Sections 2.5 and 2.6; *2.6e. Redescending M-Estimators for Scale; 2.7. Relation with Huber's Minimax Approach; Exercises and Problems; 3. ONE-DIMENSIONAL TESTS; 3.1. Introduction; 3.2. The Influence Function for Tests; 3.2a. Definition of the Influence Function; 3.2b. Properties of the Influence Function; 3.2c. Relation with Level and Power; 3.2d. Connection with Shift Estimators; 3.3. Classes of Tests; 3.3a The One-Sample Case; 3.3b. The Two-Sample Case; 3.4. Optimally Bounding the Gross-Error Sensitivity 3.5. Extending the Change-of-Variance Function to Tests |
| Record Nr. | UNINA-9910877493903321 |
| New York, : Wiley, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||