von Mises Calculus For Statistical Functionals

Inhaltsverzeichnis

• 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.