frame_ald_weight: Weighting Matrix of Quantile regression using Asymmetric...
In quokar: Quantile Regression Outlier Diagnostics with K Left Out Analysis

Description Usage Arguments Details Author(s) Examples

This function calulate the weighting matrix

1	frame_ald_weight(y, x, tau, error, iter)

`y`	dependent variable of quantile regression
`x`	design matrix of quantile regression
`tau`	quantile must be a scaler
`error`	The EM algorithm accuracy of error used in MLE estimation
`iter`	The iteration frequancy for EM algorithm used in MLE estimation

In the estimation procedure in EM algorithm, we can see that \varepsilon is inversely proportional to d_i = |y_i-x^{'}_{i}β^{(k)}_{p}|/σ. Hence, u_i(θ^{k})=\varepsilon_{-1i}(θ^{(k)}) can be interpreted as a type of weight for ith case in the estimates of β_{(k)^p}, which tends to be small for outlying observations.

Wenjing Wang wenjingwangr@gmail.com

library(ggplot2)
library(dplyr)
library(ALDqr)
data(ais)
y <- ais$BMI
x <- cbind(1, ais$LBM)
tau <-  c(0.1, 0.5, 0.9)
error <- 1e-06
iter <- 100
weights <- frame_ald_weight(y, x, tau, error, iter)
weights