Description Usage Arguments Details Value Author(s) References Examples

Compute truncated Gaussian p-value of Lee et al. (2016) with arbitrary affine selection and covariance. Z should satisfy A

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`Z` |
Observed data (assumed to follow N(mu, Sigma) with sum(eta*mu)=null_value) |

`A` |
Matrix specifiying affine inequalities AZ <= b |

`b` |
Offsets in the affine inequalities AZ <= b. |

`eta` |
Determines the target sum(eta*mu) and estimate sum(eta*Z). |

`Sigma` |
Covariance matrix of Z. Defaults to identity. |

`null_value` |
Hypothesized value of sum(eta*mu) under the null. |

`bits` |
Number of bits to be used for p-value and confidence interval calculations. Default is
NULL, in which case standard floating point calculations are performed. When not NULL,
multiple precision floating point calculations are performed with the specified number
of bits, using the R package |

This function computes selective p-values based on the polyhedral lemma of Lee et al. (2016).

`pv` |
One-sided P-values for active variables, uses the fact we have conditioned on the sign. |

`vlo` |
Lower truncation limits for statistic |

`vup` |
Upper truncation limits for statistic |

`sd` |
Standard error of sum(eta*Z) |

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Joshua Loftus, Stephen Reid

Jason Lee, Dennis Sun, Yuekai Sun, and Jonathan Taylor (2016). Exact post-selection inference, with application to the lasso. Annals of Statistics, 44(3), 907-927.

Jonathan Taylor and Robert Tibshirani (2017) Post-selection inference for math L1-penalized likelihood models. Canadian Journal of Statistics, xx, 1-21. (Volume still not posted)

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