von Mises Calculus For Statistical Functionals von L. T. Fernholz | ISBN 9780387908991

von Mises Calculus For Statistical Functionals

von L. T. Fernholz
Buchcover von Mises Calculus For Statistical Functionals | L. T. Fernholz | EAN 9780387908991 | ISBN 0-387-90899-4 | ISBN 978-0-387-90899-1

von Mises Calculus For Statistical Functionals

von L. T. Fernholz

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.