Effects of sampling on statistics of large-scale structure

Accepted for publication in MNRAS The effects of sampling are investigated on measurements of counts-in-cells in threedimensional magnitude limited galaxy surveys, with emphasis on moments of the underlying smooth galaxy density field convolved with a spherical window. A new estimator is proposed for measuring the k-th order moment 〈ρ k 〉: the weighted factorial moment ˜ Fkω. Since these statistics are corrected for the effects of the varying selection function, they can extract the moments in one pass without the need of constructing a series of volume limited samples. The cosmic error on the measurement of ˜ Fkω is computed via the the formalism of Szapudi Colombi (1996), which is generalized to include the effects of the selection function. The integral equation for finding the minimum variance weight is solved numerically, and an accurate and intuitive analytical approximation is derived ωoptimal(r) ∝ 1/∆(r), where ∆(r) is the cosmic error as a function of the distance from the observer. The resulting estimator is more accurate than the traditional method