# TG.limits: Truncation limits and standard deviation. In selectiveInference: Tools for Post-Selection Inference

## Description

Compute truncated limits and SD for use in computing p-values or confidence intervals of Lee et al. (2016). Z should satisfy A

## Usage

 `1` ```TG.limits(Z, A, b, eta, Sigma) ```

## Arguments

 `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.

## Details

This function computes the limits of truncation and the implied standard deviation in the polyhedral lemma of Lee et al. (2016).

## Value

 `vlo` Lower truncation limits for statistic `vup` Upper truncation limits for statistic `sd` Standard error of sum(eta*Z)

## Author(s)

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

## References

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)

## Examples

 ```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.limits(Z, A, b, eta, Sigma) ```

selectiveInference documentation built on Sept. 7, 2019, 9:02 a.m.