TG.limits {selectiveInference}

Truncation limits and standard deviation.

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

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

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)