Summary
This note discusses some aspects of the estimation of the density function of a univariate probability distribution. All estimates of the density function satisfying relatively mild conditions are shown to be biased. The asymptotic mean square error of a particular class of estimates is evaluated.
Received April 27, 1955.
Research carried out at the Statistical Research Center, University of Chicago, under the sponsorship of the Statistics Branch, Office of Naval Research.
The comments of R. R. Bahadur have been very helpful.
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E. Fix and J. L. Hodges, Jr., Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties, USAF School of Aviation Medicine, Project No. 21–49–004, Report No. 4.
E. Lehmann, ”Notes on the theory of estimation,” University of California, Berkeley (1950).
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Davis, R.A., Lii, KS., Politis, D.N. (2011). Remarks on Some Nonparametric Estimates of a Density Function. In: Davis, R., Lii, KS., Politis, D. (eds) Selected Works of Murray Rosenblatt. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8339-8_13
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