Multivariate Density Estimation Using Dimension Reducing Information and Tail Flattening Transformations for Truncated or Censored Data

Abstract

This paper introduces a multivariate density estimator for truncated and censored data with special emphasis on extreme values based on survival analysis. A local constant density estimator is considered. We extend this estimator by means of tail flattening transformation, dimension reducing prior knowledge and a combination of both. The asymptotic theory is derived for the proposed estimators. It shows that the extensions might improve the performance of the density estimator when the transformation and the prior knowledge is not too far away from the true distribution. A simulation study shows that the density estimator based on tail flattening transformation and prior knowledge substantially outperforms the one without prior knowledge, and therefore confirms the asymptotic results. The proposed estimators are illustrated and compared in a data study of fire insurance claims.

Keywords: censoring, Champernowne, counting process theory, multiplicative correction, nonparametric estimation, truncation

JEL Classification: C14, C34