WRegTest: Test the case weighted regression estimator by Empirical... In emplik: Empirical Likelihood Ratio for Censored/Truncated Data

Description

Use the empirical likelihood ratio and Wilks theorem to test if the regression coefficient is equal to `beta0`, by the case weighted estimation method.

The log empirical likelihood been maximized is

∑_{d=1} \log Δ F(y_i) + ∑_{d=0} \log [1-F(y_i)].

Usage

 `1` ```WRegTest(x, y, delta, beta0, psifun=function(t){t}) ```

Arguments

 `x` a matrix of size N by q. Random design matrix. `y` a vector of length N, containing the censored responses. `delta` a vector (length N) of either 1's or 0's. delta=1 means y is uncensored; delta=0 means y is right censored. `beta0` a vector of length q. The value of the regression coefficient to be tested in the linear model

.

 `psifun` the estimating function. The definition of it determines the type of estimator under testing.

Details

The above likelihood should be understood as the likelihood of the censored responses `y` and `delta`.

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 = ∑ δ_i Δ F(Y_i) X_i ( Y_i - X_i β0 )

which was described in detail in the reference below.

For median regression (Least Absolute Deviation) estimator, you should define the `psifun` as +1, -1 or 0 when t is >0, <0 or =0.

For ordinary least squares estimator, `psifun` should be the identity function psifun <- function(t)t.

Value

A list with the following components:

 `"-2LLR"` the -2 log likelihood ratio; have approximate chisq distribution under H_0. `P-val` the p-value using the chi-square approximation.

Mai Zhou.

References

Zhou, M.; Bathke, A. and Kim, M. (2012). Empirical likelihood analysis of the case weighted estimator in heteroscastic AFT model. Statistica Sinica, 22, 295-316.

Examples

 `1` ```xx <- c(28,-44,29,30,26,27,22,23,33,16,24,29,24,40,21,31,34,-2,25,19) ```

emplik documentation built on May 29, 2017, 11:44 a.m.