Abstract We develop a method originally proposed by R. A. Fisher into a general procedure, called tailoring, for deriving goodness-of-fit tests that are guaranteed to have a χ2documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$chi ^{2}$$end{document} asymptotic null distribution. The method has a robustness feature that it works correctly in testing a certain aspect of the model while some other aspect of the model may be misspecified. We apply the method to small area estimation. A connection, and difference, to the existing specification test is discussed. We evaluate performance of the tests both theoretically and empirically, and compare the performance with several existing methods. Our empirical results suggest that the proposed test is more accurate in size, and has either higher or similar power compared to the existing tests. The proposed test is also computationally less demanding than the specification test and other comparing methods. A real-data application is discussed.
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