qbj {SetTest}

Quantile of Berk-Jones statitic under the null hypothesis.

Description

Quantile of Berk-Jones statitic under the null hypothesis.

Usage

qbj(p, M, k0, k1, onesided = FALSE)

Arguments

p

- a scalar left probability that defines the quantile.

M

- correlation matrix of input statistics (of the input p-values).

k0

- search range starts from the k0th smallest p-value.

k1

- search range ends at the k1th smallest p-value.

onesided

- TRUE if the input p-values are one-sided.

Value

Quantile of BJ statistics.

References

1. Hong Zhang, Jiashun Jin and Zheyang Wu. "Distributions and Statistical Power of Optimal Signal-Detection Methods In Finite Cases", submitted.

2. Donoho, David; Jin, Jiashun. "Higher criticism for detecting sparse heterogeneous mixtures". Annals of Statistics 32 (2004).

3. Berk, R.H. & Jones, D.H. Z. "Goodness-of-fit test statistics that dominate the Kolmogorov statistics". Wahrscheinlichkeitstheorie verw Gebiete (1979) 47: 47.

See Also

stat.bj for the definition of the statistic.

Examples

## The 0.05 critical value of BJ statistic when n = 10:
qbj(p=.95, M=diag(10), k0=1, k1=5, onesided=FALSE)