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The Construction and Properties of Boundary Kernels for Smoothing Sparse Multinomials

Jianping Dong and Jeffrey S. Simonoff
Journal of Computational and Graphical Statistics
Vol. 3, No. 1 (Mar., 1994), pp. 57-66
DOI: 10.2307/1390795
Stable URL: http://www.jstor.org/stable/1390795
Page Count: 10
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The Construction and Properties of Boundary Kernels for Smoothing Sparse Multinomials
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Abstract

In recent years several authors have investigated the use of smoothing methods for sparse multinomial data. In particular, Hall and Titterington (1987) studied kernel smoothing in detail. It is pointed out here that the bias of kernel estimates of probabilities for cells near the boundaries of the multinomial vector can dominate the mean sum of squared error of the estimator for most true probability vectors. Fortunately, boundary kernels devised to correct boundary effects for kernel regression estimators can achieve the same result for these estimators. Properties of estimates based on boundary kernels are investigated and compared to unmodified kernel estimates and maximum penalized likelihood estimates. Monte Carlo evidence indicates that the boundary-corrected kernel estimates usually outperform uncorrected kernel estimates and are quite competitive with penalized likelihood estimates.

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