**Chad M. Schafer**

The observational limitations of astronomical surveys lead to
significant statistical inference challenges. One such challenge is the
estimation of luminosity functions given redshift and absolute magnitude
measurements from an irregularly truncated sample of objects. This is a
bivariate density estimation problem; we develop here a statistically
rigorous method that (1) does not assume a strict parametric form
for the bivariate density; (2) does not assume independence between
redshift and absolute magnitude (and hence allows evolution of the
luminosity function with redshift); (3) does not require dividing the
data into arbitrary bins; and (4) naturally incorporates a varying
selection function. There is a simple way of estimating the integrated
mean squared error of the estimator; smoothing parameters are selected to
minimize this quantity. Results are presented from the analysis of a
sample of quasars.

Heidi Sestrich 2006-10-16 Here is the full PDF text for this technical report. It is 610978 bytes long.