Generalized Cook's distance for each observation in quantile regression model
ALDqr_GCD(y, x, tau, error, iter)Dependent variable in quantile regression. Note that: we suppose y follows asymmetric laplace distribution.
indepdent variables in quantile regression. Note that: x is the independent variable matrix which including the intercept. That means, if the dimension of independent variables is p and the sample size is n, x is a n times p+1 matrix with the first column being one.
quantile
the EM algorithm accuracy of error used in MLE estimation
the iteration frequancy for EM algorithm used in MLE estimation
Gerneralized Cook's distance is a commonly used estimate of the influence of a data point when performing regression analysis. It involves the log-likelihood function based on the complete data and case-deletion data. To assess the influence of the \(i\)th case with estimate \(\hat{\theta}\), we compare \(\hat{\theta_(i)}\) and \(\hat{\theta}\), and if \(\hat{\theta_(i)}\) is far from \(\hat{\theta_(i)}\), then the \(i\)th case is regarded as influential. We consider here the following generalized Cook's distance: $$GCD_{i} = (\hat{\theta_{(i)}}-\hat{\theta{i}})^{'} {-Q(\hat{\theta}|\hat{\theta})} (\hat{\theta_{(i)}}-\hat{\theta{i}})$$ $$Q_{(i)}(\theta|\hat{\theta})=E_{\hat{\theta}}[l_{c}(\theta|Y_{c(i)})|y]$$ More details please refer to the paper in references
Benites L E, Lachos V H, Vilca F E.(2015)``Case-Deletion Diagnostics for Quantile Regression Using the Asymmetric Laplace Distribution,arXiv preprint arXiv:1509.05099.
ALDqr_QD