TEST manuscript No. (will be inserted by the editor) Goodness-of-fit test with a robustness feature Jiming Jiang · Mahmoud Torabi Received: July 20, 2020 / Accepted: date 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 χ 2 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 ex- isting tests. The proposed test is also computationally less demanding than the specification test and other comparing methods. A real-data application is discussed. Keywords Goodness-of-fit tests · Maple · Model diagnostics · Robustness · Small area estimation · Tailoring Mathematics Subject Classification (2010) 62F05 · 62J05 · 62D99 J. Jiang Department of Statistics, University of California, Davis, One Shields Avenue, Davis CA 95616, USA Tel.: +1-530-752-1761 Fax: +1-530-752-7099 E-mail: jimjiang@ucdavis.edu M. Torabi Department of Community Health Sciences, University of Manitoba, 750 Bannatyne Ave, Winnipeg, Manitoba, R3E 0W3, Canada Tel.: +1-204-272-3136 Fax: +1-204-789-3905 E-mail: Mahmoud.Torabi@umanitoba.ca