Description Usage Arguments Details Value Author(s) References Examples

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

1 2 3 4 5 6 | ```
TG.interval(Z, A, b, eta, Sigma=NULL, alpha=0.1,
gridrange=c(-100,100),
gridpts=100,
griddepth=2,
flip=FALSE,
bits=NULL)
``` |

`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. |

`alpha` |
Significance level for confidence intervals (target is miscoverage alpha/2 in each tail) |

`gridrange` |
Grid range for constructing confidence intervals, on the standardized scale. |

`gridpts` |
??????? |

`griddepth` |
??????? |

`flip` |
??????? |

`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 confidence intervals based on the polyhedral lemma of Lee et al. (2016).

`int` |
Selective confidence interval. |

`tailarea` |
Realized tail areas (lower and upper) for each confidence interval. |

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)

1 2 3 4 5 6 | ```
A = diag(5)
b = rep(1, 5)
Z = rep(0, 5)
Sigma = diag(5)
eta = as.numeric(c(1, 1, 0, 0, 0))
TG.interval(Z, A, b, eta, Sigma)
``` |

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