Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 30 / 2 / a / Solution

Write $m_i=\mu +{\alpha }_i$. Apart from a constant, the log-likelihood isFor each group,Thus maximum likelihood estimation sets ${\hat{m}}_i={\overline{Y}}_i$. The corner-point constraint ${\alpha }_1=0$ identifies $m_1=\mu$, givingThe baseline mean is the first group mean, rather than the grand mean, because of the chosen identifiability constraint.