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Testing the parametric form of the conditional variance in regressions based on distance covariance

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  • Hu, Yue
  • Li, Haiqi
  • Tan, Falong

Abstract

A new test based on distance covariance is proposed for testing the parametric form of the conditional variance in parametric and nonparametric regression models. Inherit from the nice properties of distance covariance, the new test is very easy to implement in practice and less effected by the dimensionality of covariates. The asymptotic properties of the test statistic are investigated under the null and alternative hypotheses. The proposed test is consistent against any alternative hypothesis and can detect some classes of local alternative hypotheses converging to the null hypothesis at the parametric rate in both the parametric and nonparametric settings. As the limiting null distribution of the test statistic is intractable, a smooth residual bootstrap is proposed to approximate the limiting null distribution. Simulation studies are conducted to assess the finite sample performance of the proposed test. A real data set is also analyzed for illustration.

Suggested Citation

  • Hu, Yue & Li, Haiqi & Tan, Falong, 2024. "Testing the parametric form of the conditional variance in regressions based on distance covariance," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:csdana:v:189:y:2024:i:c:s0167947323001627
    DOI: 10.1016/j.csda.2023.107851
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    References listed on IDEAS

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    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. A. Sen & B. Sen, 2014. "Testing independence and goodness-of-fit in linear models," Biometrika, Biometrika Trust, vol. 101(4), pages 927-942.
    3. Su, Liangjun & Ullah, Aman, 2013. "A Nonparametric Goodness-Of-Fit-Based Test For Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 29(1), pages 187-212, February.
    4. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    5. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    6. Lan Wang & Xiao-Hua Zhou, 2007. "Assessing the Adequacy of Variance Function in Heteroscedastic Regression Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1218-1225, December.
    7. Samarakoon, Nishantha & Song, Weixing, 2011. "Minimum distance conditional variance function checking in heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 579-600, March.
    8. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
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