Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 422--430

ON MULTIPLICATIVE BIAS CORRECTION IN KERNEL DENSITY ESTIMATION

By

M.C. JONES, The Open University, U.K.


D.F. SIGNORINI, Quintiles Scotland Ltd, U.K.

and

N.L. HJORT, University of Oslo, Norway

SUMMARY. Hjort and Glad (1995) present a method for semiparametric density estimation. Relative to the ordinary kernel density estimator, this technique performs much better when a parametric vehicle distribution fits the data, and otherwise performs at broadly the same level. Jones, Linton and Nielsen (1995) present a somewhat similar method for density estimation which has higher order bias for all sufficiently smooth densities. In this paper, we combine the two methods. We show that, theoretically, the desired properties of general higher order bias allied with even better performance for an appropriate vehicle model are achieved. Simulations suggest that the new estimator realises only a little of its theoretical potential in practice for small to moderately large sample sizes.

AMS (1991) subject classification. 62G07.

Key words and phrases. Bias reduction; semiparametric density estimation; smoothing.

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