Approximating Maximally Selected Statistics

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

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

Arguments

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.

Details

Approximation based on an improved Bonferroni inequality.

Value

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

References

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

Examples


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)))