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.Comment: 33 pages, 10 figures, accepted for publication in PASJ (Vol.59, No.1
in press
