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emplik (version 1.3-1)

bjtest1d: 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)

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.

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

Author

Mai Zhou.

Details

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

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

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

Run this code
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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