Efron–Petrosian integrals for doubly truncated data with covariates: An asymptotic analysis

In survival analysis, epidemiology and related fields there exists an increasing interest in statistical methods for doubly truncated data. Double truncation appears with interval sampling other schemes, refers to situations which the target variable is subject two (left right) random observation limits. Doubly data require specific corrections observational bias, this affects a variety of settings including estimation marginal multivariate distributions, regression problems, multi-state models. work Efron–Petrosian integrals are introduced. These naturally arise when goal mean general transformation involves covariates. An asymptotic representation as sum i.i.d. terms derived and, from this, consistency distributional convergence established. As by-product, uniform representations nonparametric maximum likelihood estimator its corresponding weighting process provided. Applications correlation regression, competing risks models presented. A simulation study reported too.