stepm: Romano and Wolf's (2005) StepM
In grayclhn/oosanalysis-R-library: Pseudo out-of-sample forecasting

Description Usage Arguments Details Value Author(s) References See Also Examples

Implements Romano and Wolf's StepM, a stepdown procedure for multiple hypothesis testing.

1	stepm(teststatistics, bootmatrix, lefttail, righttail)

`teststatistics`	A numeric vector, containing test statistics.
`bootmatrix`	A matrix with `length(teststatistics)` rows and an arbitrary number of columns. Each column is a different draw from the bootstrap-induced distribution of `teststatistics`.
`lefttail`	The mass to be left in the left tail of the distribution. Setting this to `NA` imposes a one-sided alternative.
`righttail`	The mass to be left in the right tail of the distribution. Setting this to `NA` imposes a one-sided alternative.

This function assumes that each element of teststatistics tests (say) mu[i] = 0 against the alternative mu[i] > 0, for i = 1,...,length(teststatistics). Romano and Wolf's (2005) StepM procedure estimates a critical value such that the probability that it is smaller than at least one statistic corresponding to a true null hypothesis is controlled at level level.

A list with the following elements:

`criticalvalues`	The estimated critical values.
`rejected`	A logical vector indicating which statistcs fall outside the critical values.

Gray Calhoun gcalhoun@iastate.edu

Calhoun, G. 2011, Documentation appendix: An asymptotically normal out-of-sample test of equal predictive accuracy for nested models. Unpublished manuscript.

Calhoun, G. 2012, A comment on "Stepwise multiple testing as formalized data snooping." Unpublished manuscript.

Romano, J. P., and Wolf, M. 2005, Stepwise multiple testing as formalized data snooping. Econometrica, 73(4), pages 1237–1292.

boot

n <- 50
nboot <- 99
d <- data.frame(x1 = rnorm(n), x2 = rnorm(n) + 1, x3 = rnorm(n))

dottests <- function(dataset)
  sapply(dataset, function(x) t.test(x)$statistic)

stepm(teststatistics = dottests(d),
      bootmatrix = replicate(nboot, dottests(d[sample(1:n, n, replace = TRUE),])),
      lefttail = NA, righttail = 0.05)