stat.tfisher.omni {TFisher}

Construct omnibus thresholding Fisher's (TFisher) p-value combination statistic.

Description

Construct omnibus thresholding Fisher's (TFisher) p-value combination statistic.

Usage

stat.tfisher.omni(p, TAU1, TAU2, M = NULL, MU = NULL, SIGMA2 = NULL,
  P0 = NULL)

Arguments

p

- input p-values from potentially correlated input sstatistics.

TAU1

- a vector of truncation parameters. Must be in non-descending order.

TAU2

- a vector of normalization parameters. Must be in non-descending order.

M

- correlation matrix of the input statistics. Default = NULL assumes independence

MU

- a vector of means of TFisher statistics. Default = NULL.

SIGMA2

- a vector of variances of TFisher statistics. Default = NULL.

P0

- a vector of point masses of TFisher statistics. Default = NULL.

Details

Let x_{i}, i = 1,...,n be a sequence of individual statistics with correlation matrix M, p_{i} be the corresponding two-sided p-values, then the TFisher statistics

TFisher_j = \sum_{i=1}^n -2\log(p_i/\tau_{2j})I(p_i\leq\tau_{1j})

, j = 1,...,d. The omnibus test statistic is the minimum p-value of these thresholding tests,

W_o = min_j G_j(Soft_j)

, where G_j is the survival function of Soft_j.

Value

omni - omnibus TFisher statistic.

pval - p-values of each TFisher tests.

References

1. Hong Zhang and Zheyang Wu. "TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values", submitted.

Examples

pval = runif(20)
TAU1 = c(0.01, 0.05, 0.5, 1)
TAU2 = c(0.1, 0.2, 0.5, 1)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2)
M = matrix(0.3,20,20) + diag(1-0.3,20)
stat.tfisher.omni(p=pval, TAU1=TAU1, TAU2=TAU2, M=M)