# EL.Huber: Empirical likelihood test for the difference of smoothed... In EL: Two-Sample Empirical Likelihood

 EL.Huber R Documentation

## Empirical likelihood test for the difference of smoothed Huber estimators

### Description

Empirical likelihood inference for the difference of smoothed Huber estimators. This includes a test for the null hypothesis for a constant difference of smoothed Huber estimators, confidence interval and EL estimator.

### Usage

```EL.Huber(X, Y, mu = 0, conf.level = 0.95,
scaleX=1, scaleY=1, VX = 2.046, VY = 2.046, k = 1.35)
```

### Arguments

 `X` a vector of data values. `Y` a vector of data values. `mu` a number specifying the null hypothesis. `conf.level` confidence level of the interval. `scaleX` the scale estimate of sample 'X'. `scaleY` the scale estimate of sample 'Y'. `VX` the asymptotic variance of initial (nonsmooth) Huber estimator for the sample 'X'. `VY` the asymptotic variance of initial (nonsmooth) Huber estimator for the sample 'Y'. `k` tuning parameter for the Huber estimator.

### Details

A common choice for a robust scale estimate (parameters scaleX and scaleY) is the mean absolute deviation (MAD).

### Value

A list of class 'htest' containing the following components:

 `estimate ` the empirical likelihood estimate for the difference of two smoothed Huber estimators. `conf.int ` a confidence interval for the difference of two smoothed Huber estimators. `p.value ` the p-value for the test. `statistic ` the value of the test statistic. `method ` the character string 'Empirical likelihood smoothed Huber estimator difference test'. `null.value ` the specified hypothesized value of the mean difference 'mu' under the null hypothesis. `data.name ` a character string giving the names of the data.

### Author(s)

E. Cers, J. Valeinis

### References

J. Valeinis, E. Cers. Extending the two-sample empirical likelihood. To be published. Preprint available at http://home.lanet.lv/~valeinis/lv/petnieciba/EL_TwoSample_2011.pdf.

F. Hampel, C. Hennig and E. A. Ronchetti (2011). A smoothing principle for the Huber and other location M-estimators, Computational Statistics & Data Analysis, 55(1), 324-337.

`EL.means`

### Examples

```X <- rnorm(100)
Y <- rnorm(100)
t.test(X, Y)
EL.means(X, Y)
EL.Huber(X, Y)
```

EL documentation built on Dec. 28, 2022, 2:47 a.m.