WRegEst {emplik}R Documentation

Compute the casewise weighted regression estimator for AFT model

Description

For the AFT model, this function computes the case weighted estimator of beta. Either the least squares estimator or the regression quantile estimator.

Usage

WRegEst(x, y, delta, LS=TRUE, tau=0.5)

Arguments

x a matrix of size N by q.
y a vector of length N, containing the censored responses.
delta a vector (length N) of either 1's or 0's. d=1 means y is uncensored; d=0 means y is right censored.
LS a logical value. If TRUE then the function will return the least squares estimator. If FALSE then the function will return the regression quantile estimator, with quantile specified by tau.
tau a scalar, between 0 and 1. The quantile to be used in quantile regression. If LS=TRUE, then it is ignored.

Details

Due to the readily available minimizer, we only provide least squares and quantile regression here. However, in the companion testing function WRegTest the user can supply a self defined psi function, corresponding to the general M-estimation in the regression modeling. (since there is no minimization needed)

The estimator is the minimizer of

sum_{i=1}^n w_i rho (Y_i - X_i b)

Assuming a correlation model Y_i = X_i β + σ(X_i) ε_i .

Value

The estimator hat β.

Author(s)

Mai Zhou.

References

Zhou, M.; Bathke, A. and Kim, M. (2006). Empirical likelihood analysis of the Heteroscastic AFT model. Dept. of Statistics, Univ. of Kentucky Tech. Report.

Examples

if(require("rankreg", quietly = TRUE)) {
####library(rankreg)
data(smallcell)
WRegEst(x=cbind(1,smallcell[,1],smallcell[,2]), 
        y=smallcell[,3], delta=smallcell[,4]) 
####################################################
#### you should get         x1         x2         x3
####                 -59.22126 -488.41306   16.03259
####################################################
WRegEst(x=cbind(1,smallcell[,1],smallcell[,2]), 
        y=log10(smallcell[,3]), delta=smallcell[,4], LS=FALSE) 
########################################################
#### you should get      
####     [1]     2.603342985  -0.263000044  0.003836832
########################################################
xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19)
}

[Package emplik version 0.9-5 Index]