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 $$ \sum_{d=1} \log \Delta F(e_i) + \sum_{d=0} \log [1-F(e_i)] .$$
bjtest1d(y, d, x, beta)A list with the following components:
the -2 loglikelihood ratio; have approximate chi square distribution under \(H_o\).
the log empirical likelihood, under estimating equation.
the log empirical likelihood of the Kaplan-Meier of e's.
the probabilities that max the empirical likelihood under estimating equation constraint.
a vector of length N, containing the censored responses.
a vector of either 1's or 0's. d=1 means y is uncensored. d=0 means y is right censored.
a vector of length N, covariate.
a number. the regression coefficient to be tested in the model y = x beta + epsilon
Mai Zhou.
In the above likelihood, \( e_i = y_i - x * beta \) is the residuals.
Similar to bjtest( ), but only for 1-dim beta.
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.
xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19)
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