pconnorm: pconnorm .

In epsiwal: Exact Post Selection Inference with Applications to the Lasso

Description

CDF of the conditional normal variate.

Usage

pconnorm(y, A, b, eta, mu = NULL, Sigma = NULL, Sigma_eta = Sigma
  %*% eta, eta_mu = as.numeric(t(eta) %*% mu), lower.tail = TRUE,
  log.p = FALSE)

Arguments

y	an n vector, assumed multivariate normal with mean μ and covariance Σ.
A	an k \times n matrix of constraints.
b	a k vector of inequality limits.
eta	an n vector of the test contrast, η.
mu	an n vector of the population mean, μ. Not needed if eta_mu is given.
Sigma	an n \times n matrix of the population covariance, Σ. Not needed if Sigma_eta is given.
Sigma_eta	an n vector of Σ η.
eta_mu	the scalar η^{\top}μ.
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].
log.p	logical; if TRUE, probabilities p are given as log(p).

Details

Computes the CDF of the truncated normal conditional on linear constraints, as described in section 5 of Lee et al.

Let y be multivariate normal with mean μ and covariance Σ. Conditional on Ay <= b for conformable matrix A and vector b we compute the CDF of a truncated normal maximally aligned with η. Inference depends on the population parameters only via eta'mu and Sigma eta, and only these need to be given.

The test statistic is aligned with y, meaning that an output p-value near one casts doubt on the null hypothesis that eta'mu is less than the posited value.

Value

The CDF.

Note

An error will be thrown if we do not observe A y <= b.

Author(s)

Steven E. Pav [e-mail]

References

Lee, J. D., Sun, D. L., Sun, Y. and Taylor, J. E. "Exact post-selection inference, with application to the Lasso." Ann. Statist. 44, no. 3 (2016): 907-927. doi:10.1214/15-AOS1371. https://arxiv.org/abs/1311.6238

See Also

the confidence interval function, ci_connorm.

epsiwal documentation built on July 2, 2019, 5:07 p.m.