mtest {GammaTest}R Documentation

The M-test: Judging the Reliability of the Gamma Statistic

Description

Computes and plots successive Gamma statistics and V ratios over an increasing number of data points M.

Usage

mtest(data, start=20, mask=seq(from=1, to=1, length=(length(data[1,])-1)), step=1, p=10, eps=0.00, ...)

Arguments

data Input/Output data.frame, where the outputs are in the last column.
start Burn-in period, must be greater than the number of near neighbours p.
mask The input inclusion/exclusion on which to calculate the Gamma statistics. The default is all the 1s i.e. include all inputs.
step The number of data points to increment.
p The sample of near neighbours
eps The error bound for calculating approximate near neighbours. The default is 0 meaning the exact near neighbours are calculated.
... Graphical device parameters (e.g. colour, labelling, titles, etc)

Details

The proof of the Gamma test assures us that as M tends to infinity the noise estimate given by the Gamma test will converge on the true noise variance with probability one. However, this does not give an indication of how many data points are required to give an accurate estimate of the noise. In order to achieve this, the Gamma statistic is computed for increasing M. By plotting the Gamma statistics over M it can be seen whether the graph appears to be approaching a stable asymptote.

If M-test graph stabilises then this indicates that there is enough data to construct a smooth model, which is of considerable benefit neural network users because the number of data points required for the training set can be determined prior to modelling.

Value

{results}{The returned Gamma statistics} {vratios}{The returned V ratios}

Author(s)

Samuel E. Kemp. To report any bugs or suggestions please email: sekemp@glam.ac.uk

References

Stefansson A., Koncar N. and Jones A. J. (1997), A note on the gamma test. Neural Computing Applications, 5:131-133.

Evans D., Jones A. J. and Schmidt W. (2002). Asymptotic moments of near neighbour distance distributions. Proc. Roy. Soc. Lond. Series A, 458(2028):2839-2849.

Evans D. and Jones A. J. (2002), A proof of the gamma test. Proc. Roy. Soc. Lond. Series A, 458(2027):2759-2799.

For papers and Gamma test related material visit http://users.cs.cf.ac.uk:81/Antonia.J.Jones/GammaArchive/IndexPage.htm

See Also

gammatest mask2input

Examples

# Example on an AR(1) process
ts.sim  <- arima.sim(500, model=list(ar=0.9), sd=sqrt(1))
ts.io   <- mask2input(1, as.matrix(ts.sim)) # Create input/output dataset
mt              <- mtest(ts.io)

# Noisy Sine wave example
x <- seq(length=500, from=-2*pi, to=2*pi)
y <- sin(x) + rnorm(500, sd=sqrt(0.075)) # Set the variance of the noise to 0.075.
xy <- data.frame(x,y)                    # Create an input/output dataset.
mt <- mtest(xy)

[Package GammaTest version 1.1 Index]