This paper considers estimates of multidimensional density functions based on a bounded and bandlimited weight function. The asymptotic behavior of quadratic functions of density function estimates useful in setting up a test of goodness of fit of the density function is determined. A test of independent is also given. The methods use a Poissonization of sample size. The estimates considered are appropriate if interested in estimating density functions or determining local deviations from a given density function.
"A Quadratic Measure of Deviation of Two-Dimensional Density Estimates and A Test of Independence." Ann. Statist. 3 (1) 1 - 14, January, 1975. https://doi.org/10.1214/aos/1176342996