pconnorm {epsiwal}

pconnorm .

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 \mu and covariance \Sigma.

A

an k \times n matrix of constraints.

b

a k vector of inequality limits.

eta

an n vector of the test contrast, \eta.

mu

an n vector of the population mean, \mu. Not needed if eta_mu is given.

Sigma

an n \times n matrix of the population covariance, \Sigma. Not needed if Sigma_eta is given.

Sigma_eta

an n vector of \Sigma \eta.

eta_mu

the scalar \eta^{\top}\mu.

lower.tail

logical; if TRUE (default), probabilities are P[X \le 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 \mu and covariance \Sigma. Conditional on Ay \le b for conformable matrix A and vector b we compute the CDF of a truncated normal maximally aligned with \eta. Inference depends on the population parameters only via \eta^{\top}\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^{\top}\mu is less than the posited value.

Value

The CDF.

Note

An error will be thrown if we do not observe A y \le 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.