Neyman-Scott incidental parameter problem
= Neyman-Scott incidental parameter problem
{c}
A growing number of nuisance parameters can prevent a <maximum-likelihood estimator> of a common parameter from being <consistent>. With two independent normal observations of mean $\mu_i$ per group, the profiled variance estimate $\sum_i(X_{1i}-X_{2i})^2/(4n)$ tends to half the true variance, because each unknown mean is estimated using only two observations.