emplik (version 1.3-1)

WRegEst: 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)

Value

The estimator \( \hat \beta\).

Arguments

x

a matrix of size N by q.

y

a vector of length N, containing the censored responses. Usually the log of the original observed failure times.

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 quantile regression estimator, with the quantile level specified by tau.

.

tau

a scalar, between 0 and 1. The quantile to be used in quantile regression. If tau=0.5 then it is the median regression. If LS=TRUE, then it is ignored.

Author

Mai Zhou.

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 $$ Y_i = X_i \beta + \sigma(X_i) \epsilon_i $$, where \(\rho( )\) is either the square or the absolute value function.

References

Zhou, M.; Bathke, A. and Kim, M. (2012). Empirical likelihood analysis of the Heteroscastic Accelerated Failure Time model. Statistica Sinica, 22, 295-316.

Examples

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
########################################################