ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 62G07, 62H17 Jiang, Renfang The mean sum of squared error of a wavelet based multinomial density estimator A wavelet-based estimator is introduced to smooth multinomial data. If the underlying density has rth bounded derivative, the mean sum of squared error of the estimator is O(K^{−1}N^{−2r/(2r+1)}), where K is the number of cells and N is the total number of cell counts. No boundary conditions are needed, and the smoothness condition can be relaxed to piecewise smoothness. Reference: P. Hall and P. Patil, Formulae for mean integrated squared error of nonlinear wavelet-based density estimators, Ann. Statist. 23 (1995), 905–928.