On the linearity truncated bivariate normal distribution

Motivated by a problem in archaeological data analysis, we examine through
simulation the effect of linear truncation on density estimation in the bivariate
normal distribution. It is shown that the estimation procedure performs poorly
when the truncation line is parallel to the minor axis of the elliptical contours
of the distribution. The estimation also worsens with increasing correlation and
increasing disparity in the values of the variances in the distribution. Reconstruction
of the bivariate normal distribution is best achieved when truncation is
parallel to the major axis and there is only about 10% of the data that is missing.