Compositional (version 1.4)

Exponential empirical likelihood hypothesis testing for two mean vectors: Exponential empirical likelihood hypothesis testing for two mean vectors

Description

Exponential empirical likelihood hypothesis testing for two mean vectors.

Usage

eel.test2(y1, y2, tol = 1e-07, R = 0, graph = FALSE)

Arguments

y1

A matrix containing the Euclidean data of the first group.

y2

A matrix containing the Euclidean data of the second group.

tol

The tolerance level used to terminate the Newton-Raphson algorithm.

R

If R is 0, the classical chi-sqaure distribution is used, if R = 1, the corrected chi-sqaure distribution (James, 1954) is used and if R = 2, the modified F distribution (Krishnamoorthy and Yanping, 2006) is used. If R is greater than 3 bootstrap calibration is performed.

graph

A boolean variable which is taken into consideration only when bootstrap calibration is performed. IF TRUE the histogram of the bootstrap test statistic values is plotted.

Value

A list including:

test

The empirical likelihood test statistic value.

modif.test

The modified test statistic, either via the chi-square or the F distribution.

dof

Thre degrees of freedom of the chi-square or the F distribution.

pvalue

The asymtptoci or the bootstrap p-value.

mu

The estimated common mean vector.

runtime

The runtime of the bootstrap calibration.

Details

Exponential empirical likelihood is a non parametric hypothesis testing procedure for one sample. The generalisation to two (or more samples) is via searching for the mean vector that minimises the sum of the two test statistics.

References

Jing Bing-Yi and Andrew TA Wood (1996). Exponential empirical likelihood is not Bartlett correctable. Annals of Statistics 24(1): 365-369.

G.S. James (1954). Tests of Linear Hypothese in Univariate and Multivariate Analysis when the Ratios of the Population Variances are Unknown. Biometrika, 41(1/2): 19-43

Krishnamoorthy K. and Yanping Xia (2006). On Selecting Tests for Equality of Two Normal Mean Vectors. Multivariate Behavioral Research 41(4): 533-548.

Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.

Amaral G.J.A., Dryden I.L. and Wood A.T.A. (2007). Pivotal bootstrap methods for k-sample problems in directional statistics and shape analysis. Journal of the American Statistical Association 102(478): 695-707.

Preston S.P. and Wood A.T.A. (2010). Two-Sample Bootstrap Hypothesis Tests for Three-Dimensional Labelled Landmark Data. Scandinavian Journal of Statistics 37(4): 568-587.

See Also

el.test2, maovjames, maov, hotel2T2, james, comp.test

Examples

eel.test2( iris[1:25, 1:4], iris[26:50, 1:4], R = 0 )
eel.test2( iris[1:25, 1:4], iris[26:50, 1:4], R = 1 )
eel.test2( iris[1:25, 1:4], iris[26:50, 1:4], R = 2 )