ci_connorm_max: ci_connorm_max .

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

ci_connorm_max .

Description

Confidence intervals on normal mean, conditioning on the max.

Usage

ci_connorm_max(
  yk,
  yk1,
  sigma = 1,
  rho = 0,
  p = c(level/2, 1 - (level/2)),
  level = 0.05
)

Arguments

yk	the observed maximum value, y_k.
yk1	a vector of the other observed values, y_{k1}, or just the scalar second largest value.
sigma	the common standard deviation.
rho	the common correlation.
p	a vector of probabilities for which we return equivalent \eta^{\top}\mu.
level	if p is not given, we set it by default to c(level/2,1-level/2).

Details

Computes the confidence interval of unknown mean of a normal vector conditional on the one element being the maximum.

Let y be multivariate normal with unknown mean \mu and known covariance \Sigma. We assume that \Sigma is compound symmetric with common variance \sigma^2 and common correlation \rho.

Conditional on y_k \ge y_i for all i, we compute the confidence interval of \mu_k.

Value

The values of \mu_k which have the corresponding CDF.

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 CDF function, pconnorm, the MLE function, mle_connorm_max, the more general version, ci_connorm.

epsiwal documentation built on June 10, 2026, 9:06 a.m.