Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Semiparametric Bivariate Density Estimation with Irregularly Truncated Data

Publication Date

September, 2006

Publication Type

Tech Report


Chad M. Schafer


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.