bjtest {emplik}  R Documentation 
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 [1F(e_i)];
where e_i
are the residuals.
bjtest(y, d, x, beta)
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

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.
A list with the following components:
"2LLR" 
the 2 loglikelihood ratio; have approximate chisq
distribution under 
logel2 
the log empirical likelihood, under estimating equation. 
logel 
the log empirical likelihood of the KaplanMeier of e's. 
prob 
the probabilities that max the empirical likelihood under estimating equation. 
Mai Zhou.
Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66 42936.
Zhou, M. and Li, G. (2008). Empirical likelihood analysis of the BuckleyJames estimator. Journal of Multivariate Analysis 99, 649664.
Zhou, M. (2016) Empirical Likelihood Method in Survival Analysis. CRC Press.
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