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Biometrika 1998 85(1):131-138; doi:10.1093/biomet/85.1.131
© 1998 by Biometrika Trust
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Semiparametric smoothing for discrete data

M. J. FADDY and M. C. JONES

Centre for Statistics, Department of Mathematics, The University of Queensland Brisbane, Queensland 4072, Australia mjf{at}maths.uq.edu.au
Department of Statistics, The Open University Walton Hall, Milton Keynes MK7 6AA, U.K. m.c.jones{at}open.ac.uk

A method for semiparametric smoothing of discrete data is proposed. The method consists of the repeated application of a Markov chain transition matrix constructed so as to have a given standard discrete parametric vehicle model as its stationary distribution. Theory and practical examples suggest that the approach yields improved performance over fully nonparametric methods when the vehicle model is a good one and otherwise provides a method comparable to fully nonparametric smoothers. An automatic choice of the amount of smoothing is proposed and used.

Key Words: Bionomil • Markov chain • Poisson • Probability function estimate • Smoothing parameter selection • Stationary distribution


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