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von Mises Calculus For Statistical Functionals
von L. T. FernholzInhaltsverzeichnis
- I. Introduction.
- II. Von Mises’ Method.
- 2.1 Statistical functionals.
- 2.2 Von Mises expansions.
- 2.3 Frééchet derivatives.
- III. Hadamard Differentiation.
- 3.1 Definitions of differentiability.
- 3.2 An implicit function theorem.
- IV. Some Probability Theory on C[0,1] and D[0,1].
- 4.1 The spaces C[0,1] and D[0,1].
- 4.2 Probability theory on C[0,1].
- 4.3 Probability theory on D[0,1].
- 4.4 Asymptotic Normality.
- V. M-, L-, and R-Estimators.
- 5.1 M-estimators.
- 5.2 L-estimators.
- 5.3 R-estimators.
- 5.4 Modifications of elements of D[0,1].
- VI. Calculus on Function Spaces.
- 6.1 Differentiability theorems.
- 6.2 An implicit function theorem for statistical functionals.
- VII. Applications.
- 7.1 M-estimators.
- 7.2 L-estimators.
- 7.3 R-estimators.
- 7.4 Functionals on C[0,1]: sample quantiles.
- 7.5 Truncated d. f.’s and modified estimators.
- VIII. Asymptotic Efficiency.
- 8.1 Asymptotic efficiency and Hadamard differentiability.
- 8.2 Asymptotically efficient estimators of location.
- References.
- List of symbols.