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Lack-of-fit tests based on weighted ratio of residuals and variances

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Abstract

This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.

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Authors and Affiliations

  1. Center for Applied Statistics, School of Statistics, Remin University of China, Beijing, 100872, China

    Maozai Tian

  2. School of Science, Hubei University of Technology, Wuhan, 430068, China

    Youxi Luo

  3. School of Statistics, Remin University of China, Beijing, 100872, China

    Youxi Luo, Yunan Su & Yan Fan

  4. School of Mathematics, Yunnan Normal University, Kunming, 650092, China

    Junlin Han

Authors
  1. Maozai Tian
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  2. Youxi Luo
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  3. Yunan Su
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  4. Yan Fan
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  5. Junlin Han
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Corresponding author

Correspondence to Maozai Tian.

Additional information

The research was partially supported by the Major Project of Humanities Social Science Foundation of Ministry of Education under Grant No. 08JJD910247, Key Project of Chinese Ministry of Education under Grant No. 108120, National Natural Science Foundation of China under Grant No. 11271368, Beijing Natural Science Foundation under Grant No. 1102021, the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China under Grant Nos. 10XNL018 and 11XNH107.

This paper was recommended for publication by Editor Guohua ZOU.

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Tian, M., Luo, Y., Su, Y. et al. Lack-of-fit tests based on weighted ratio of residuals and variances. J Syst Sci Complex 25, 1202–1214 (2012). https://doi.org/10.1007/s11424-012-0193-3

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  • DOI: https://doi.org/10.1007/s11424-012-0193-3

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