Description Usage Arguments Details Value References Examples

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

1 2 | ```
stat.tfisher.omni(p, TAU1, TAU2, M = NULL, MU = NULL, SIGMA2 = NULL,
P0 = NULL)
``` |

`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. |

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*.

omni - omnibus TFisher statistic.

pval - p-values of each TFisher tests.

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

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)
``` |

```
$omni
[1] 0.4666071
$pvals
[1] 1.0000000 1.0000000 0.6071336 0.4666071
$omni
[1] 0.4488222
$pvals
[1] 1.0000000 1.0000000 0.5060848 0.4488222
```

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