R: Approximating Maximally Selected Statistics

pLausen94 {maxstat} | R Documentation

## Approximating Maximally Selected Statistics

### Description

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

### Usage

    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)))

[Package maxstat version 0.7-25 Index]