rp.test: The k random projections test for normality.

In nortsTest: Assessing Normality of Stationary Process

The k random projections test for normality.

Description

Performs the random projection test for normality. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.

Usage

rp.test(y, k = 1, FDR = TRUE, pars1 = c(100,1), pars2  = c(2,7),
               seed = NULL)

Arguments

y	a numeric vector or an object of the ts class containing a stationary time series.
k	an integer that determines the '2k' random projections are used for every type of test. The 'pars1' argument generates the first 'k' projections, and 'pars2' generates the later 'k' projections. By default, k = 1.
FDR	a logical value for mixing the p.values using a False discovery rate method. If FDR = TRUE, then the p.values are mixed using Benjamin and Yekutieli (2001) False discovery Rate method for dependent procedures, on the contrary, it applies Benjamini and Hochberg (1995) procedure. By default, FDR = TRUE.
pars1	an optional real vector with the shape parameters of the beta distribution used for the first 'k' random projections By default, pars1 = c(100,1) where, shape1 = 100 and shape2 = 1.
pars2	an optional real vector with the shape parameters of the beta distribution used to compute the last 'k' random projections. By default, pars2 = c(2,7) where, shape1 = 2 and shape2 = 7.
seed	An optional seed to use.

Details

The random projection test generates '2k' random projections of 'y'. Applies Epps statistics to the odd projections and Lobato and Velasco’s statistics to the even ones. Computes the '2k' p.values using an asymptotic chi-square distribution with two degrees of freedom. Finally, mixes the p.values using a false discover rate procedure. By default, mixes the p.values using Benjamin and Yekutieli’s (2001) method.

The function uses beta distributions for generating the '2k' random projections. By default, uses a beta(shape1 = 100,shape = 1) distribution contained in pars1 argument to generate the first 'k' projections. For the later 'k' projections the functions uses a beta(shape1 = 2,shape = 7) distribution contained in pars2 argument.

The test was proposed by Nieto-Reyes, A.,Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

A list with class "h.test" containing the following components:

statistic:	an integer value with the amount of projections per test.
parameter:	a text that specifies the p.value mixing FDR method.
p.value:	the FDR mixed p-value for the test.
alternative:	a character string describing the alternative hypothesis.
method:	a character string “k random projections test”.
data.name:	a character string giving the name of the data.

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics. 29, 1165–1188. Doi:10.1214/aos/1013699998.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 75, 800–803. Doi:10.2307/2336325.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

See Also

lobato.test, epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
rp.test(y)

nortsTest documentation built on May 29, 2024, 10:05 a.m.