Description Usage Arguments Details References See Also
Generalized Cook's distance for each observation in quantile regression model
1 | ALDqr_GCD(y, x, tau, error, iter)
|
y |
Dependent variable in quantile regression. Note that: we suppose y follows asymmetric laplace distribution. |
x |
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. |
tau |
quantile |
error |
the EM algorithm accuracy of error used in MLE estimation |
iter |
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 ith case with estimate \hat{θ}, we compare \hat{θ_(i)} and \hat{θ}, and if \hat{θ_(i)} is far from \hat{θ_(i)}, then the ith case is regarded as influential. We consider here the following generalized Cook's distance:
GCD_{i} = (\hat{θ_{(i)}}-\hat{θ{i}})^{'} {-Q(\hat{θ}|\hat{θ})} (\hat{θ_{(i)}}-\hat{θ{i}})
Q_{(i)}(θ|\hat{θ})=E_{\hat{θ}}[l_{c}(θ|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.
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