Estimating a density and its derivatives via the minimum distance method

DOI10.1007/BF00318908zbMath0644.62039MaRDI QIDQ1102656

Lestaw Gajek

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

rate of convergenceminimum distance estimatorsdensity estimatorsmean integrated square errorestimation of derivativesLp-estimationminimum penalized distance estimatorsrates of strong consistency

Mathematics Subject Classification ID

Nonparametric estimation (62G05)

Related Items (3)

A function fitting method ⋮ Invariance principles for deconvoluting kernel density estimation ⋮ Upper bounds for the \(L_ 1\)-risk of the minimum \(L_ 1\)-distance regression estimator

Cites Work

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• Spline smoothing: The equivalent variable kernel method
• On improving density estimators which are not bona fide functions
• Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz
• Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
• On estimating a density using Hellinger distance and some other strange facts
• Estimation of Distribution Density Belonging to a Class of Entire Functions
• A Lower Bound on the Risks of Non-Parametric Estimates of Densities in the Uniform Metric
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Sharp rates of convergence of maximum likelihood estimators in nonparametric models

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