pLausen94: Approximating Maximally Selected Statistics
In maxstat: Maximally Selected Rank Statistics

Description Usage Arguments Details Value References Examples

Approximates the probability that a maximally selected rank statistic is greater or equal to b.

1 2	pLausen94(b, N, minprop=0.1, maxprop=0.9, m=NULL) qLausen94(p, N, minprop=0.1, maxprop=0.9, m=NULL)

`b`	quantile.
`p`	probability.
`N`	number of observations.
`minprop`	at least `minprop`*100% of the observations in the first group.
`maxprop`	not more than `minprop`*100% of the observations in the first group.
`m`	a integer vector containing the sample sizes in the first groups for each cutpoint considered. If `is.null(m)` a continuous predictor is assumed.

Approximation based on an improved Bonferroni inequality.

The probability that, under the hypothesis of independence, a maximally selected statistic greater equal b is observed.

Worsley, K.J. (1982), An Improved Bonferroni Inequality and Applications. Biometrika, 69, 297–302

Lausen, B. (1990), Maximal Selektierte Rangstatistiken. Dissertation. Universit\"at Dortmund

Lausen, B., Sauerbrei, W. & Schumacher, M. (1994). Classification and Regression Trees (CART) used for the exploration of prognostic factors measured on different scales. in: P. Dirschedl & R. Ostermann (Eds), Computational Statistics, Heidelberg, Physica-Verlag, 483–496

p <- pLausen94(2.5, 20, 0.25, 0.75)

# Lausen 94, page 489

if (round(p, 3) != 0.073) stop("error checking pLausen94")

# the same

p2 <- pLausen94(2.5, 200, 0.25, 0.75, m=seq(from=50, to=150, by=10))

stopifnot(all.equal(round(p,3), round(p2,3)))