EL.Huber {EL}

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.

See Also

EL.means

Examples

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