Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis

A method of counts-in-cells analysis of galaxy distribution is investigated with arbitrary smoothing functions in obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, considering a series of $m$-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second moments of counts-in-cells as a first step. We analytically derive the covariance matrix among different smoothing scales of cells, taking into account possible overlaps between cells. We find that the Epanechnikov kernel of $m=1$ is better than top-hat and Gaussian smoothing functions in estimating cosmological parameters. As an example, we estimate expected parameter bounds which comes only from the analysis of second moments of galaxy distributions in a survey which is similar to the Sloan Digital Sky Survey.