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An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models

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  • Lan Wang
  • Michael Akritas
  • Ingrid Van Keilegom

Abstract

For the heteroscedastic nonparametric regression model Yni=m (xni)+σ (xni) εni, i=1, …, n, we discuss a novel method for testing some parametric assumptions about the regression function m. The test is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Asymptotic normality of the test statistic is established under the null hypothesis and suitable local alternatives. The similarity of the form of the test statistic to that of the classical F-statistic in analysis of variance allows easy and fast calculation. Simulation studies demonstrate that the new test possesses satisfactory finite-sample properties.

Suggested Citation

  • Lan Wang & Michael Akritas & Ingrid Van Keilegom, 2008. "An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(5), pages 365-382.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:365-382
    DOI: 10.1080/10485250802066112
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    Cited by:

    1. Behzad Alimoradian & Jeffrey Jakubiak & Stephane Loisel & Yahia Salhi, 2023. "Understanding Key Drivers of Participant Cash Flows for Individually Managed Stable Value Funds," Risks, MDPI, vol. 11(8), pages 1-27, August.
    2. Brian Gray & Vyacheslav Lyubchich & Yulia Gel & James Rogala & Dale Robertson & Xiaoqiao Wei, 2016. "Estimation of river and stream temperature trends under haphazard sampling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 89-105, March.
    3. Lihong Wang, 2020. "Lack of fit test for long memory regression models," Statistical Papers, Springer, vol. 61(3), pages 1043-1067, June.
    4. Fabio Di Nunno & Marco De Matteo & Giovanni Izzo & Francesco Granata, 2023. "A Combined Clustering and Trends Analysis Approach for Characterizing Reference Evapotranspiration in Veneto," Sustainability, MDPI, vol. 15(14), pages 1-23, July.
    5. Lyubchich, Vyacheslav & Gel, Yulia R., 2016. "A local factor nonparametric test for trend synchronism in multiple time series," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 91-104.

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