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Biometrika 1978 65(3):521-528; doi:10.1093/biomet/65.3.521
© 1978 by Biometrika Trust
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Univariate density estimation by orthogonal series

H. D. BRUNK

Department of Statistics, Oregon State University Corvallis

Orthogonal series estimators of univariate densities are proposed that are derived from and motivated by kernel estimators optimal in Whittle's (1958) sense. A preliminary fit of the data from within a one or two parameter class of densities plays the role of a prior mean density. The ratio of the true density and the prior mean density is assumed to have a series expansion in terms of functions orthogonal with respect to the prior mean density. Coefficients of terms of the series are given a joint prior distribution according to which they are independent, with zero means.

Key Words: Kernel estimator • Nonparametric density estimation • Orthogonal series estimator


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