Nonparametric estimation of the cross ratio function

Steven Abrams (), Paul Janssen, Jan Swanepoel and Noël Veraverbeke
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Steven Abrams: Hasselt University
Paul Janssen: Hasselt University
Jan Swanepoel: North-West University
Noël Veraverbeke: Hasselt University

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 3, No 6, 801 pages

Abstract: Abstract The cross ratio function (CRF) is a commonly used tool to describe local dependence between two correlated variables. Being a ratio of conditional hazards, the CRF can be rewritten in terms of (first and second derivatives of) the survival copula of these variables. Bernstein estimators for (the derivatives of) this survival copula are used to define a nonparametric estimator of the cross ratio, and asymptotic normality thereof is established. We consider simulations to study the finite sample performance of our estimator for copulas with different types of local dependency. A real dataset is used to investigate the dependence between food expenditure and net income. The estimated CRF reveals that families with a low net income relative to the mean net income will spend less money to buy food compared to families with larger net incomes. This dependence, however, disappears when the net income is large compared to the mean income.

Keywords: Asymptotic distribution; Bernstein estimation; Copula; Cross ratio function; Hazard rate (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10463-019-00709-3

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