Q-function distance for each observation in quantile regression model
ALDqr_QD(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 is one.
Quantile
The EM algorithm accuracy of error used in MLE estimation
The iteration frequancy for EM algorithm used in MLE estimation
Measure of the influence of the \(i\)th case is the following Q-distance function, similar to the likelihood distance \(LD_{i}\) (Cook and Weisberg, 1982), defined as
$$QD_{i} = 2{Q(\hat{\theta}|\hat{\theta})-Q(\hat{\theta_{(i)}})}$$
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_GCD