Semiparametric Bivariate Density Estimation with Irregularly Truncated Data

This work develops an estimator for the bivariate density given a sample of data truncated to a non-rectangular region. Such inference problems occur in various fields; the motivating application here was a problem in astronomy. The approach is semiparametric, combining a nonparametric local likelihood density estimator with a simple parametric form to account for the dependence of the two random variables. Large sample theory for M-estimators is utilized to approximate the distribution for the estimator. A method is described for approximating the integrated mean squared error of the estimator; smoothing parameters can be selected to minimize this quantity. Results are described from the analysis of data from the measurements of quasars. A Fortran implementation is available, along with an R wrapper function.