bjtest {emplik}

Test the Buckley-James estimator by Empirical Likelihood

Description

Use the empirical likelihood ratio and Wilks theorem to test if the regression coefficient is equal to beta.

The log empirical likelihood been maximized is

\sum_{d=1} \log \Delta F(e_i) + \sum_{d=0} \log [1-F(e_i)];

where e_i are the residuals.

Usage

bjtest(y, d, x, beta)

Arguments

y

a vector of length N, containing the censored responses.

d

a vector (length N) of either 1's or 0's. d=1 means y is uncensored; d=0 means y is right censored.

x

a matrix of size N by q.

beta

a vector of length q. The value of the regression coefficient to be tested in the model y_i = \beta x_i + \epsilon_i

Details

The above likelihood should be understood as the likelihood of the error term, so in the regression model the error epsilon should be iid.

This version can handle the model where beta is a vector (of length q).

The estimation equations used when maximize the empirical likelihood is

0 = \sum d_i \Delta F(e_i) (x \cdot m[,i])/(n w_i)

which was described in detail in the reference below.

Value

A list with the following components:

"-2LLR"

the -2 loglikelihood ratio; have approximate chisq distribution under H_o.

logel2

the log empirical likelihood, under estimating equation.

logel

the log empirical likelihood of the Kaplan-Meier of e's.

prob

the probabilities that max the empirical likelihood under estimating equation.

Author(s)

Mai Zhou.

References

Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66 429-36.

Zhou, M. and Li, G. (2008). Empirical likelihood analysis of the Buckley-James estimator. Journal of Multivariate Analysis 99, 649-664.

Zhou, M. (2016) Empirical Likelihood Method in Survival Analysis. CRC Press.

Examples

xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19)