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Efficient estimation of semiparametric copula models for bivariate survival data(Journal of Multivariate Analysis, Elsevier BV, 2014-01) [Article]A semiparametric copula model for bivariate survival data is characterized by a parametric copula model of dependence and nonparametric models of two marginal survival functions. Efficient estimation for the semiparametric copula model has been recently studied for the complete data case. When the survival data are censored, semiparametric efficient estimation has only been considered for some specific copula models such as the Gaussian copulas. In this paper, we obtain the semiparametric efficiency bound and efficient estimation for general semiparametric copula models for possibly censored data. We construct an approximate maximum likelihood estimator by approximating the log baseline hazard functions with spline functions. We show that our estimates of the copula dependence parameter and the survival functions are asymptotically normal and efficient. Simple consistent covariance estimators are also provided. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2013 Elsevier Inc.
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Linear factor copula models and their properties(Scandinavian Journal of Statistics, Wiley, 2018-04-25) [Article]We consider a special case of factor copula models with additive common factors and independent components. These models are flexible and parsimonious with O(d) parameters where d is the dimension. The linear structure allows one to obtain closed form expressions for some copulas and their extreme-value limits. These copulas can be used to model data with strong tail dependencies, such as extreme data. We study the dependence properties of these linear factor copula models and derive the corresponding limiting extreme-value copulas with a factor structure. We show how parameter estimates can be obtained for these copulas and apply one of these copulas to analyse a financial data set.
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Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials(Econometrics and Statistics, Elsevier BV, 2019-09-09) [Article]Tools for characterizing non-linear spectral dependence between spontaneous brain signals are developed, based on the use of parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded by various microelectrodes. The following major questions are addressed. The first is to determine changepoints in the regime within a microelectrode for a given frequency band based on a difference between the cumulative distribution functions modeled for each epoch (small window of time). The proposed approach is an iterative algorithm which compares each successive bivariate copulas on all the epochs range, using a bivariate Kolmogorov-Smirnov statistic. The second is to determine if such changes are present only in some microelectrodes versus generalized across the entire network. These issues are addressed by comparing Vine-copulas models fitted for each epoch. The necessary framework is provided and the effectiveness of the methods is shown through the results for the local field potential data analysis of a rat.