# stat.tpm.omni: Construct omnibus truncated product method statistic. In TFisher: Optimal Thresholding Fisher's P-Value Combination Method

## Description

Construct omnibus truncated product method statistic.

## Usage

 `1` ```stat.tpm.omni(p, TAU1, M = NULL) ```

## Arguments

 `p` - input p-values. `TAU1` - a vector of truncation parameters. Must be in non-descending order. `M` - correlation matrix of the input statistics. Default = NULL assumes independence.

## 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 truncated product method statistics

TPM_j = ∑_{i=1}^n -2\log(p_i)I(p_i≤qτ_{1j})

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

W_o = min_j G_j(TPM_j)

, where G_j is the survival function of TPM_j.

## Value

omni - omnibus truncated product method statistic.

pval - p-values of each truncated product method tests.

## References

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

## Examples

 ```1 2 3 4 5``` ```pval = runif(20) TAU1 = c(0.01, 0.05, 0.5, 1) stat.tpm.omni(p=pval, TAU1=TAU1) M = matrix(0.3,20,20) + diag(1-0.3,20) stat.tpm.omni(p=pval, TAU1=TAU1, M=M) ```

TFisher documentation built on May 2, 2019, 12:20 p.m.