• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.515-529
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• 1998

Burman (1987) and Hall and Titterington (1987) studied kernel smoothing for sparse multinomial data in detail. Both of their estimators for cell probabilities are sparse asymptotic consistent under some restrictive conditions on the true cell probabilities. Dong and Simonoff (1994) adopted boundary kernels to relieve the restrictive conditions. We propose a local linear kernel estimator which is popular in nonparametric regression to estimate cell probabilities. No boundary adjustment is necessary for this estimator since it adapts automatically to estimation at the boundaries. It is shown that our estimator attains the optimal rate of convergence in mean sum of squared error under sparseness. Some simulation results and a real data application are presented to see the performance of the estimator.