A simple estimator of two-dimensional copulas, with applications
File(s)
Accepted version
Author(s)
Anderson, Eddie
Prokhorov, Artem
Zhu, Yajing
Type
Journal Article
Abstract
Copulas are distributions with uniform marginals. Non‐parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi‐spaced grid a natural starting point. However, the mixed‐integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non‐parametric MLE of B‐spline coefficients on possibly non‐equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.
Date Issued
2020-05-05
Date Acceptance
2020-05-01
Citation
Oxford Bulletin of Economics and Statistics, 2020, 82 (6), pp.1375-1412
ISSN
0305-9049
Publisher
Wiley
Start Page
1375
End Page
1412
Journal / Book Title
Oxford Bulletin of Economics and Statistics
Volume
82
Issue
6
Copyright Statement
© 2020 The Department of Economics, University of Oxford and John Wiley & Sons Ltd. This is the accepted version of the following article: Anderson, E., Prokhorov, A. and Zhu, Y. (2020), A Simple Estimator of Two‐Dimensional Copulas, with Applications1. Oxf. Bull. Econ. Stat., 82: 1375-1412, which has been published in final form at https://doi.org/10.1111/obes.12371
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000530377800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Social Sciences
Science & Technology
Physical Sciences
Economics
Social Sciences, Mathematical Methods
Statistics & Probability
Business & Economics
Mathematical Methods In Social Sciences
Mathematics
MAXIMUM-LIKELIHOOD-ESTIMATION
DENSITY-ESTIMATION
SPLINE ESTIMATION
DEPENDENCE
MODEL
SERIES
Publication Status
Published
Date Publish Online
2020-05-05