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

## Description

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

## Usage

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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))) ```

maxstat documentation built on May 2, 2019, 2:44 a.m.