mle_connorm_max: mle_connorm_max .

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

mle_connorm_max .

Description

Maximum likelihood estimate of normal mean, conditioning on the max.

Usage

mle_connorm_max(yk, yk1, sigma = 1, rho = 0, ...)

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.
...	dots are passed to uniroot.

Details

Computes the maximum likelihood estimate 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 maximum likelihood estimate of \mu_k.

Value

The maximum likelihood estimate of \mu_k.

Author(s)

Steven E. Pav [e-mail]

References

Reid, S., Taylor, J. and Tibshirani, R. "Post-selection point and interval estimation of signal sizes in Gaussian samples." Can. J. Statistics. 45, no. 2 (2017): 128-148. doi:10.1002/cjs.11320. https://arxiv.org/abs/1405.3340

See Also

the confidence interval function, ci_connorm_max, the CDF function, pconnorm, the more general version, mle_connorm.

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