R: Approximating Maximally Selected Statistics

pLausen92 {maxstat} | R Documentation

## Approximating Maximally Selected Statistics

### Description

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

### Usage

    pLausen92(b, minprop=0.1, maxprop=0.9)
    qLausen92(p, minprop=0.1, maxprop=0.9)

### Arguments

`b` | quantile.
`p` | probability.
`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.

### Details

Large sample approximation by Miller and Siegmund (1982) based on a Brownian bridge, cf. Lausen and Schumacher (1992).

### Value

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

### References

Miller, R. and Siegmund, D. (1982), Maximally Selected Chi Square Statistics. Biometrics, 38, 1011–1016

Lausen, B. and Schumacher, M. (1992), Maximally Selected Rank Statistics. Biometrics, 48, 73–85

### Examples

    # Compute quantiles. Should be equal to Table 2 in Lausen and Schumacher

    load(file.path(system.file(package = "maxstat"), "results", "LausenTab2.rda"))

    a <- rev(c(0.01, 0.025, 0.05, 0.1))
    prop <- rbind(c(0.25, 0.75), c(0.4, 0.6), c(0.1, 0.9), c(0.4, 0.9))
    Quant <- matrix(rep(0, length(a)*nrow(prop)), nrow=length(a))

    for (i in 1:length(a)) {
      for (j in 1:nrow(prop)) {
        Quant[i,j] <- qLausen92(a[i], minprop=prop[j,1], maxprop=prop[j,2])
      }
    }

    Quant <- round(Quant, 3)
    rownames(Quant) <- a
    colnames(Quant) <- c("A2575", "A46", "A19", "A49")
    Quant <- as.data.frame(Quant)
    rownames(LausenTab2) <- a

    Quant

    LausenTab2

    if(!all.equal(LausenTab2, Quant)) stop("error checking pLausen92")

[Package maxstat version 0.7-25 Index]