Celebratio Mathematica — Rosenblatt

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P. A. W. Lewis, L. H. Liu, D. W. Robinson, and M. Rosenblatt: “Empirical sampling study of a goodness of fit statistic for density function estimation,” pp. 159–174 in Multivariate analysis IV (Dayton, OH, 16–21 June 1975). Edited by P. R. Krishnaiah. 1977. Zbl 0399.62039 incollection

The distribution of a measure of the distance between a probability density function and its estimate is examined through empirical sampling methods. The estimate of the density function is that proposed by Rosenblatt using sums of weight functions centered at the observed values of the random variables. The weight function in all cases was triangular, but both uniform and Cauchy densities were tried for different sample sizes and bandwidths. The simulated distributions look as if they could be approximated by Gamma distributions, in many cases. Some assessment can also be made of the rate of convergence of the moments and the distribution of the measure to the limiting moments and distribution, respectively.

Paruchuri R. Krishnaiah	Related
Peter A. W. Lewis	Related
Li Hung Liu	Related
Derek W. Robinson	Related