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Statistical Estimation of Density Functions

M. S. Bartlett
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 25, No. 3 (Sep., 1963), pp. 245-254
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25049271
Page Count: 10
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Statistical Estimation of Density Functions
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Abstract

The optimum choice of weighting function for smoothing sample density functions is discussed in the cases: (i) probability densities; (ii) spectral densities. It is shown that the bias contribution to the mean-square error can in principle be eliminated to any required order, though the resulting theoretical gain in efficiency may not be realised except for very large samples. The relation with recent work by Rosenblatt, Daniels and Parzen is noted. The further problem of estimating the spectra of stationary point processes is also considered.

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