Empirical Sampling Investigation of a Global Measure of Fit of Probability Density Functions.

The distribution of a measure of distance between a probability density function and its estimate is examined through Monte Carlo 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 used in all cases was triangular, but both uniform and Cauchy densities were tried for different sample sizes and bandwidths. The simulated distributions appear in all cases to be close to Gamma distributions, but it has not been possible to relate the parameters to the population characteristics or to the window shape and bandwidth. Author