A Statistical Method for Estimating Luminosity Functions Using Truncated Data

The observational limitations of astronomical surveys lead to significant statistical inference challenges. One such challenge is the estima measurements from an irregularly truncated sample of objects. This is a bivariate density estimation problem; we develop here a statist for the bivariate density; (2) does not assume independence between redshift and absolute magnitude (and hence allows evolution of the into arbitrary bins; and (4) naturally incorporates a varying selection function. We accomplish this by decomposing the bivariate density log phi (z,M) = f(z) + g(M) + h(z, M, theta ), where f and g are estimated nonparametrically and h takes an assumed parametric form. There is a simple way of estimating the integr selected to minimize this quantity. Results are presented from the analysis of a sample of quasars.