H.test {FieldSim}R Documentation

Performs Hurst parameter test for random Gaussian field

Description

The function H.test performs the test "the Hurst parameter of Z is equal to H" against the alternative hypothesis.

Usage

H.test(Z,H,alternative="two.sided",conf.level=0.95)

Arguments

Z a matrix of size (n x n). Z is the matrix associated with the sample path of one fractional Brownian field. n must be of the form 2^{J}+1 where J is a positive integer. So Z[i,j] is the value of the process at the point ((i-1)2^{-J},(j-1)2^{-J}).
H a real in ]0,1[. H is the Hurst parameter of the fractional Brownian field to be tested.
alternative a character string specifying the alternative hypothesis, must be one of '"two.sided"' (default), '"greater"' or '"less"'.
conf.level confidence level of the interval

Details

The test is build using the asymptotic distribution of the quadratic variations given in Brouste et al. (2006)

Value

A list with the following components:

statistic the value of the test statistic,
p.value the p-value for the test,
conf.int a confidence interval for the Hurst parameter,
gamma2 the constant of the variance used in the test.

Author(s)

Alexandre Brouste (http://ljk.imag.fr/membres/Alexandre.Brouste) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).

References

A. Brouste, J. Istas and S. Lambert-Lacroix (2007). On Gaussian random fields simulations.

See Also

fieldsim, midpoint.

Examples

# load FieldSim library
library(FieldSim)

# Simulation
# H=0.3
res <- midpoint(H=0.3,nblevel=8)
# Test "H=0.3" against "H!=3"
H.test(res$Z,H=0.3)

[Package FieldSim version 1.2 Index]