Nonparametric Bivariate Estimation with Randomly Truncated Observations

Abstract

This chapter focuses on the nonparametric estimation of the bivariate hazard and distribution functions (d.f.) when observations are subject to random truncation. Estimation of bivariate distribution and hazard functions is discussed, and as an application of the results on bivariate d.f., bivariate kernel density estimation is presented. The chapter highlights randomly truncated models, which are conveniently used to model several aspects of AIDS data, such as the incubation time, which is defined as the time from infection to the onset of the disease or the time from the onset of AIDS until death; the time from infection to seroconversion; or in insurance applications, the reporting lags, which is the time between when an accident happens and when it is reported to the insurance company. A few results for the univariate truncation model are also presented.