Lower Bounds and Aggregation in Density Estimation
نویسنده
چکیده
In this paper we prove the optimality of an aggregation procedure. We prove lower bounds for aggregation of model selection type of M density estimators for the Kullback-Leibler divergence (KL), the Hellinger’s distance and the L1-distance. The lower bound, with respect to the KL distance, can be achieved by the on-line type estimate suggested, among others, by Yang (2000a). Combining these results, we state that logM/n is an optimal rate of aggregation in the sense of Tsybakov (2003), where n is the sample size.
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ورودعنوان ژورنال:
- Journal of Machine Learning Research
دوره 7 شماره
صفحات -
تاریخ انتشار 2006