Project R-12611

Bernstein-based estimation of the cross-ratio function (Research)

The cross-ratio function (CRF) is a commonly used local dependence measure for the association between two variables, such as infection times in infectious disease epidemiology, failure times in survival analysis or lifetimes in reliability theory. Being a ratio of conditional hazards, the CRF can be rewritten in terms of (first and second order derivatives of) the joint survival function of these random variables. Parametric and nonparametric estimators for the CRF have been proposed in the literature in the context of bivariate right-censored time-to-event data. These existing estimators are, however, either based on very strong parametric assumptions regarding the underlying association structure (in terms of copula family or frailty distribution) for these variables, or these are of little practical use due to their rough behaviour. This project aims to (i) develop a novel flexible estimator of the CRF, based on Bernstein polynomials, and investigate its finite sample properties (in simulation studies) as well as its asymptotic properties (by proving, in particular, asymptotic distribution) when censoring is present; (ii) propose an estimator that overcomes problems at the boundary of the domain; (iii) propose data-driven bandwidth (of the kernel) and order (of the Bernstein polynomials) selectors. This project takes a new nonparametric look at the estimation of the CRF and contributes with new statistical methodology.

01 January 2022 - 31 December 2025