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On two recent papers of Y. Kanazawa

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  • Jones, M. C.

Abstract

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".

Suggested Citation

  • Jones, M. C., 1995. "On two recent papers of Y. Kanazawa," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 269-271, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:3:p:269-271
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    References listed on IDEAS

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    1. Kanazawa, Yuichiro, 1993. "Hellinger distance and Akaike's information criterion for the histogram," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 293-298, July.
    2. Kanazawa, Yuichiro, 1993. "Hellinger distance and Kullback--Leibler loss for the kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 315-321, November.
    3. Hall, Peter, 1983. "On near neighbour estimates of a multivariate density," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 24-39, March.
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