CMStatistics 2015: Start Registration
View Submission - CMStatistics
B0608
Title: Parametric maximum likelihood inference for copula models with dependently left-truncated data Authors:  Takeshi Emura - The Institute of Statistical Mathematics (Japan) [presenting]
Chi-Hung Pan - National Central University (Taiwan)
Abstract: Traditionally, most literature on the left-truncated samples considers statistical inference by assuming that left-truncation time $L$ is independent of the lifetime $X$. However, dependence between $L$ and $X$ occurs, for instance in a community health and a field reliability study. A copula-based parametric model is considered for dependent truncation. Then we consider the maximum likelihood estimator (MLE) of the unknown parameters. To calculate the MLE, a key technical challenge is to obtain the form of the inclusion probability $Pr(L\leq X)$ and its partial derivatives with respect to parameters. We first show that, under the copula model on $(L, X)$, the probability $Pr(L\leq X)$ is expressed as a Reimman integral of the $h-$function on the unit interval. With these new expressions, we propose the Newton-Raphson algorithm to maximize the log-likelihood and the Hessian matrix to calculate standard errors. Simulations are conducted to examine the performance of the proposed method. Real data from a field reliability study on the brake pad lifetimes are analyzed for illustration.