Cross-validation and the smoothing of orthogonal series density estimators

DOI10.1016/0047-259X(87)90001-7zbMath0619.62033MaRDI QIDQ1089698

Hall, Peter

Publication date: 1987

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

consistencyefficiencymean square errorleast-squares cross-validationorthogonal functionsunbiasednessasymptotically optimalcosine seriesHermite seriesmean integrated square errorcross-validatory policysequential-seriessmoothed orthogonal series density estimatessmoothing policytwo- parameter smoothing

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Nonparametric inference (62G99)

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Estimating multivariate latent-structure models, Nonparametric density estimation and bandwidth selection with B-spline bases: a novel Galerkin method, Uniform consistency of automatic and location-adaptive delta-sequence estimators, Density estimation with laguerre series and censored samples, Pairwise interaction function estimation of stationary Gibbs point processes using basis expansion, Spline local basis methods for nonparametric density estimation, Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes, Adaptive orthogonal series density estimation for small samples, Convergence of Hermite Series Density Estimators Under Conditions of Weak Dependence, NONPARAMETRIC DENSITY ESTIMATION BY B-SPLINE DUALITY, Nonparametric Wavelet Regression for Binary Response

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