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.

Author(s)

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]