Asymptotic bias and variance for a general class of varying bandwidth density estimators

DOI10.1007/BF01203834zbMath0855.62028MaRDI QIDQ1917636

Ola G. Hössjer

Publication date: 9 February 1997

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

zbMATH Keywords

asymptotic expansionrecursive formulatransformation kernel density estimatorpilot estimatorTaylor series approximationsbias orderleading biasnearest neighbour type estimatorSimpson's formula approximationsvarying bandwidth estimators

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

Cites Work

• Von Mises calculus for statistical functionals
• Variable window width kernel estimates of probability densities
• Exact mean integrated squared error
• Variable kernel density estimation
• Bias reduction in kernel density estimation by smoothed empirical transformations
• Variable location and scale kernel density estimation
• On bandwidth variation in kernel estimates. A square root law
• Improved variable window kernel estimates of probability densities
• Asymptotics for the transformation kernel density estimator
• On nonparametric kernel density estimates
• On the bias of variable bandwidth curve estimators
• Taylor series approximations of transformation kernel density estimators
• Variable Kernel Estimates of Multivariate Densities
• A note on bias reduction in variable‐kernel density estimates
• A simple bias reduction method for density estimation
• A Nonparametric Estimate of a Multivariate Density Function

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