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Date : | Wednesday March 27, 2002. | Time : | 3:30pm |
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Address | Burke Science Building | |
Room: | 138 |
In terms of the cumulative distribution function the algorithm is shown to coincide with the self-consistency algorithms of Efron (1967), Turnbull (1976), and Li et al. (1997), as the window size of the kernel shrinks to zero. It modifies these algorithms by introducing kernel smoothing at each iteration. Viewing the iterative scheme as a generalized EM algorithm permits a natural interpretation of the estimator as being close to the ideal kernel density estimate where the data is not censored in any way. Simulation results support the conjecture that kernel smoothing at every iteration does not effect convergence. In addition, comparison to the standard kernel density estimate, based on smoothing Turnbull's estimator, reflect favourably on the proposed estimator for all criteria considered. Use of the estimator for smoothing histograms, hazard estimation and scatterplot smoothing is also considered.
This is joint work with Thierry Duchesne of the Department of Statistics at University of Toronto.