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Biometrika 1991 78(3):511-519; doi:10.1093/biomet/78.3.511
© 1991 by Biometrika Trust
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Kernel density estimation for length biased data

M. C. JONES

Department of Statistics, The Open University Milton Keynes MK7 6AA, U.K.

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems such as density derivative estimation.

Key Words: Density estimation • Nonparametric maximum likelihood estimator • Smoothing • Weighted distribution


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