A0470
Title: EM estimation of the B-spline Copula with penalized log-likelihood function
Authors: Xiaoling Dou - Japan Womens University (Japan) [presenting]
Satoshi Kuriki - The Institute of Statistical Mathematics (Japan)
Gwo Dong Lin - Academia Sinica (Taiwan)
Donald Richards - Pennsylvania State University (United States)
Abstract: The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. A modified EM algorithm is developed to maximize the penalized log-likelihood function, wherein the smoothly clipped absolute deviation (SCAD) penalty function is used for the penalization term. Simulation studies are conducted to demonstrate the stability of the proposed numerical procedure, show that penalization yields estimates with smaller mean-square errors when the true parameter matrix is sparse, and provide methods for determining tuning parameters and model selection. As an example is analyzed a data set consisting of birth and death rates from 237 countries, available at the website "Our World in Data", and the marginal density and distribution functions of those rates are estimated together with all parameters of our B-spline copula model.
