Non-parametric applications of an infinite dimensional convolution theorem

DOI10.1007/BF00535344zbMath0571.62031MaRDI QIDQ3687512

P. W. Millar

Publication date: 1985

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

efficient estimationstatistical functionalsspectral functionsempirical distributionquantile functionsminimum distance functionalsHajék-Le Cam convolution theoreminfinite dimensional convolution theoremM functionalsshift experiments in abstract Wiener spaces

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (12)

Efficient estimation of functionals of the spectral density of stationary Gaussian fields ⋮ An infinite dimensional convolution theorem with applications to random censoring and missing data models ⋮ Statistical inference for stationary linear models with tapered data ⋮ The convolution theorem for estimating linear functionals in indirect nonparametric regression models ⋮ Efficient estimation of spectral functionals for continuous-time stationary models ⋮ Robust estimation for continuous-time linear models with memory ⋮ An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility ⋮ Comparison of location models for stochastic processes ⋮ Some developments in semiparametric statistics ⋮ Stein 1956: Efficient nonparametric testing and estimation ⋮ Unnamed Item ⋮ The statistical work of Lucien Le Cam.

Cites Work

• Unnamed Item
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• The minimum distance method of testing
• Estimated sampling distributions: The bootstrap and competitors
• Estimating a distribution function
• Central limit theorems for empirical measures
• Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques
• Approximation Theorems of Mathematical Statistics
• A General Approach to the Optimality of Minimum Distance Estimators
• Efficient robust estimates in parametric models
• Robust estimation via minimum distance methods
• On the Efficiency of a Class of Non-Parametric Estimates
• Asymptotic minimax theorems for the sample distribution function
• Asymptotic inference in stationary Gaussian time-series
• WILLIAM F. FRIEDMAN'S TRANSCRIPTION OF THE VOYNICH MANUSCRIPT
• Sufficiency and Approximate Sufficiency
• On Estimation of the Spectral Function of a Stationary Gaussian Process
• A characterization of limiting distributions of regular estimates
• Convergence of Quantile and Spacings Processes with Applications
• Contiguity of Probability Measures
• Equivalent Comparisons of Experiments

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