An optimal approach for hypothesis testing in the presence of incomplete data

The adverse effect of small sample sizes, excessive nonresponse rate, and high dimensionality on likelihood ratio test statistic can be reduced by integrating with respect to a prior distribution. If information regarding the prior is too general (for example, only a parametric family can be specified), this distribution can be chosen from a principle of the most powerful testing. We propose the integrated most powerful test in the presence of missing data. This test can be used as a viable alternative to the maximum likelihood.