TG.limits: 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.
Value
vlo
Lower truncation limits for statistic
vup
Upper truncation limits for statistic
sd
Standard error of sum(eta*Z)
Details
This function computes the limits of truncation and the implied
standard deviation in the polyhedral lemma of Lee et al. (2016).
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)