Jones, M. C.
On two recent papers of Y. Kanazawa.
Statistics and Probability Letters, 24(3),
In two recent papers in this journal, Kanazawa (1993a, b) has described asymptotic equivalences between smoothing parameters minimising certain risk functions for histograms and kernel density estimators, respectively. In the current note, we (i) describe some well-known heuristic equivalences (known also to Kanazawa, but not mentioned in either paper) which explain why results are as they are, and (ii) put forward the more usual opposing views to Kanazawa's claim that his results “force us to entertain the possibility that the [Hellinger distance], not the conventional [integrated squared error], be the standard distance-based measure of discrepancy in density estimation”.
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