Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 32 / 3 / a

Let $Y$ denote the full data and $R$ the pattern of indicators, with $R_j=1$ for an observed component and $R_j=0$ for a missing one. For each fixed pattern $r$, split the data as $y=(y_{\mathrm{obs}}(r),y_{\mathrm{mis}}(r))$. The missing at random condition isHere $\psi$ parameterizes the missingness mechanism. Equivalently its conditional probability, with the observed data fixed, is constant over all possible completions of the missing data. The restriction is pattern-specific because the observed components depend on $r$. Missing at random allows missingness to depend on observed values; missing completely at random imposes independence from all the data.