# stat.tfisher.omni: Construct omnibus thresholding Fisher's (TFisher) p-value... In TFisher: Optimal Thresholding Fisher's P-Value Combination Method

## Description

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

## Usage

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

 ```1 2 3 4 5 6``` ```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) ```

### Example output

```\$omni
 0.4666071

\$pvals
 1.0000000 1.0000000 0.6071336 0.4666071

\$omni
 0.4488222

\$pvals
 1.0000000 1.0000000 0.5060848 0.4488222
```

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