bjtest1d {emplik} R Documentation

## Test the Buckley-James estimator by Empirical Likelihood, 1-dim only

### Description

Use the empirical likelihood ratio and Wilks theorem to test if the regression coefficient is equal to beta. For 1-dim beta only.

The log empirical likelihood been maximized is

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

### Usage

bjtest1d(y, d, x, beta)


### Arguments

 y a vector of length N, containing the censored responses. d a vector of either 1's or 0's. d=1 means y is uncensored. d=0 means y is right censored. x a vector of length N, covariate. beta a number. the regression coefficient to be tested in the model y = x beta + epsilon

### Details

In the above likelihood,  e_i = y_i - x * beta  is the residuals.

Similar to bjtest( ), but only for 1-dim beta.

### Value

A list with the following components:

 "-2LLR" the -2 loglikelihood ratio; have approximate chi square 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 constraint.

Mai Zhou.

### References

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

Owen, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90-120.

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

### Examples

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 1.1-1 Index]