Algorithm MCAP
input:
Monte Carlo profile evaluated at ϕ1:K
Local quadratic regression smoother, S
Smoothing parameter, λ
Confidence level, 1 − α
output:
Cut-off, δ, for a Monte Carlo profile likelihood confidence interval
algorithm:
Fit a local quadratic smoother,
Obtain
Obtain regression weights w1:K for the evaluation of at
Fit a linear regression model, , with weights w1:K
Obtain regression estimates and
Obtain regression covariances , ,
Let
Let χα be the (1 − α) quantile of the χ-square distribution on one degree of freedom
Let