Exponential empirical likelihood for a one sample mean vector hypothesis testing {mvhtests} | R Documentation |
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Description
Exponential empirical likelihood for a one sample mean vector hypothesis testing.
Usage
eel.test1(x, mu, tol = 1e-06, R = 1)
Arguments
x |
A matrix containing Euclidean data. |
mu |
The hypothesized mean vector. |
tol |
The tolerance value used to stop the Newton-Raphson algorithm. |
R |
The number of bootstrap samples used to calculate the p-value. If R = 1 (default value), no bootstrap calibration is performed |
Details
Exponential empirical likelihood or exponential tilting was first introduced by Efron (1981) as a way to perform a "tilted" version of the bootstrap for the one sample mean hypothesis testing. Similarly to the empirical likelihood, positive weights , which sum to one, are allocated to the observations, such that the weighted sample mean
is equal to some population mean
, under the
. Under
the weights are equal to
, where
is the sample size. Following Efron (1981), the choice of
will minimize the Kullback-Leibler distance from
to
subject to the constraint . The probabilities take the form
and the constraint becomes
A numerical search over is required. Under
, where
denotes the number of variables. Alternatively the bootstrap p-value may be computed.
Value
A list including:
p |
The estimated probabilities. |
lambda |
The value of the Lagrangian parameter |
iter |
The number of iterations required by the newton-Raphson algorithm. |
info |
The value of the log-likelihood ratio test statistic along with its corresponding p-value. |
runtime |
The runtime of the process. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
References
Efron B. (1981) Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics, 9(2): 139–158.
Jing B.Y. and Wood A.T.A. (1996). Exponential empirical likelihood is not Bartlett correctable. Annals of Statistics, 24(1): 365–369.
Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.
See Also
el.test1, hotel1T2, james, hotel2T2, maov, el.test2
Examples
x <- as.matrix( iris[, 1:4] )
eel.test1(x, numeric(4) )
el.test1(x, numeric(4) )