We study the problem of multiple hypothesis testing for multidimensional data
when inter-correlations are present. The problem of multiple comparisons is
common in many applications. When the data is multivariate and correlated,
existing multiple comparisons procedures based on maximum likelihood estimation
could be prohibitively computationally intensive. We propose to construct
multiple comparisons procedures based on composite likelihood statistics. We
focus on data arising in three ubiquitous cases: multivariate Gaussian, probit,
and quadratic exponential models. To help practitioners assess the quality of
our proposed methods, we assess their empirical performance via Monte Carlo
simulations. It is shown that composite likelihood based procedures maintain
good control of the familywise type I error rate in the presence of
intra-cluster correlation, whereas ignoring the correlation leads to erratic
performance. Using data arising from a diabetic nephropathy study, we show how
our composite likelihood approach makes an otherwise intractable analysis
possible