Robust StatisticsJohn Wiley & Sons, 2004 - 308 стор. The first systematic, book-length treatment of the subject. Begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. Stresses concepts. Provides selected numerical algorithms for computing robust estimates, as well as convergence proofs. Tables contain quantitative robustness information for a variety of estimates. |
Зміст
GENERALITIES | 1 |
THE WEAK TOPOLOGY AND ITS METRIZATION 200 | 20 |
THE BASIC TYPES OF ESTIMATES | 43 |
ASYMPTOTIC MINIMAX THEORY FOR ESTIMATING | 73 |
SCALE ESTIMATES | 107 |
MULTIPARAMETER PROBLEMS IN PARTICULAR | 127 |
7 | 142 |
REGRESSION | 153 |
ROBUSTNESS OF DESIGN | 243 |
EXACT FINITE SAMPLE RESULTS | 253 |
MISCELLANEOUS TOPICS | 286 |
REFERENCES | 294 |
| 301 | |
| 302 | |
Загальні терміни та фрази
2-alternating Analysis approximately arbitrary Assume assumptions asymptotic variance asymptotically normal bias bounded breakdown point compact continuous convergence convex convex function corresponding covariance Data defined density derivative deviation differentiable distribution F distribution functions e-contamination equivalent estimates of location Example Exhibit F(dx finite sample Fisher information follows gross error Hampel hence Huber IC(x implies inequality influence function interval Lemma linear functional location estimates M-estimate matrix median median absolute deviation metric minimax minimax tests minimizing monotone neighborhood Neyman-Pearson lemma normal distribution Note observations obtain outliers P₁ parameter particular probability measures problem Prohorov Proof random variables regression residuals respectively Robust estimation Robust regression sample median satisfies Second Edition Section sequence set function side conditions solution Stochastic sufficient symmetric test statistic theorem theory tion topology translation invariant underlying distribution unique variance ratio weak topology x₁