Smoothing spline density estimation from doubly truncated data

TL;DR

This paper develops a smoothing spline density estimator tailored for doubly truncated data, addressing sampling bias and demonstrating its effectiveness through simulations and real data applications.

Contribution

It introduces a corrected penalized likelihood approach for density estimation from doubly truncated data, with theoretical analysis and practical validation.

Findings

The estimator effectively corrects sampling bias in doubly truncated data.

Simulation results show improved accuracy over traditional methods.

Application to real datasets demonstrates practical utility.

Abstract

In Astronomy, Survival Analysis and Epidemiology, among many other fields, doubly truncated data often appear. Double truncation generally induces a sampling bias, so ordinary estimators may be inconsistent. In this paper, smoothing spline density estimation from doubly truncated data is investigated. For this purpose, an appropriate correction of the penalized likelihood that accounts for the sampling bias is considered. The theoretical properties of the estimator are discussed, and its practical performance is evaluated through simulations. Two real datasets are analyzed using the proposed method for illustrative purposes. Comparison to kernel density smoothing is included.