pphi {SetTest}

calculate the left-tail probability of phi-divergence under general correlation matrix.

Description

calculate the left-tail probability of phi-divergence under general correlation matrix.

Usage

pphi(q, M, k0, k1, s = 2, t = 30, onesided = FALSE, method = "ecc", ei = NULL)

Arguments

q

- quantile, must be a scalar.

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.

s

- the phi-divergence test parameter.

t

- numerical truncation parameter.

onesided

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

method

- default = "ecc": the effective correlation coefficient method in reference 2. "ave": the average method in reference 3, which is an earlier version of reference 2. The "ecc" method is more accurate and numerically stable than "ave" method.

ei

- the eigenvalues of M if available.

Value

Left-tail probability of the phi-divergence statistics.

References

1. Hong Zhang, Jiashun Jin and Zheyang Wu. "Distributions and power of optimal signal-detection statistics in finite case", IEEE Transactions on Signal Processing (2020) 68, 1021-1033 2. Hong Zhang and Zheyang Wu. "The general goodness-of-fit tests for correlated data", Computational Statistics & Data Analysis (2022) 167, 107379 3. Hong Zhang and Zheyang Wu. "Generalized Goodness-Of-Fit Tests for Correlated Data", arXiv:1806.03668.

Examples

M = toeplitz(1/(1:10)*(-1)^(0:9)) #alternating polynomial decaying correlation matrix
pphi(q=2, M=M, k0=1, k1=5, s=2)
pphi(q=2, M=M, k0=1, k1=5, s=2, method = "ecc")
pphi(q=2, M=M, k0=1, k1=5, s=2, method = "ave")
pphi(q=2, M=diag(10), k0=1, k1=5, s=2)