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A joint test for parametric specification and independence in nonlinear regression models

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  • Shuo Li
  • Yundong Tu

Abstract

This paper develops a testing procedure to simultaneously check (i) the independence between the error and the regressor(s), and (ii) the parametric specification in nonlinear regression models. This procedure generalizes the existing work of Sen and Sen [“Testing Independence and Goodness-of-fit in Linear Models,” Biometrika, 101, 927–942.] to a regression setting that allows any smooth parametric form of the regression function. We establish asymptotic theory for the test procedure under both conditional homoscedastic error and heteroscedastic error. The derived tests are easily implementable, asymptotically normal, and consistent against a large class of fixed alternatives. Besides, the local power performance is investigated. To calibrate the finite sample distribution of the test statistics, a smooth bootstrap procedure is proposed and found work well in simulation studies. Finally, two real data examples are analyzed to illustrate the practical merit of our proposed tests.

Suggested Citation

  • Shuo Li & Yundong Tu, 2019. "A joint test for parametric specification and independence in nonlinear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1202-1215, November.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:10:p:1202-1215
    DOI: 10.1080/07474938.2018.1536101
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    Cited by:

    1. Fan, Caiyun & Lu, Wenbin & Zhou, Yong, 2021. "Testing error heterogeneity in censored linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).

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