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Testing for a constant coefficient of variation in nonparametric regression by empirical processes

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  • Holger Dette
  • Mareen Marchlewski
  • Jens Wagener

Abstract

In the common nonparametric regression model, we consider the problem of testing the hypothesis that the coefficient of the scale and location function is constant. The test is based on a comparison of the standardized (by a local linear estimate of the scale function) observations with their mean. We show weak convergence of a centered version of this process to a Gaussian process under the null hypothesis and the alternative and use this result to construct a test for the hypothesis of a constant coefficient of variation in the nonparametric regression model. A small simulation study is also presented to investigate the finite sample properties of the new test. Copyright The Institute of Statistical Mathematics, Tokyo 2012

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  • Holger Dette & Mareen Marchlewski & Jens Wagener, 2012. "Testing for a constant coefficient of variation in nonparametric regression by empirical processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1045-1070, October.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:5:p:1045-1070
    DOI: 10.1007/s10463-011-0346-5
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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. Holger Dette & Kay Pilz, 2009. "On the estimation of a monotone conditional variance in nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 111-141, March.
    3. Holger Dette & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2009. "Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 782-799, December.
    4. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    5. Tong, Howell & Yao, Qiwei, 2000. "Nonparametric estimation of ratios of noise to signal in stochastic regression," LSE Research Online Documents on Economics 6324, London School of Economics and Political Science, LSE Library.
    6. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    7. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
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    Cited by:

    1. Van Keilegom, Ingrid, 2013. "Discussion on: "An updated review of Goodness-of-Fit tests for regression models" (by W. Gonzales-Manteiga and R.M. Crujeiras)," LIDAM Discussion Papers ISBA 2013008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Escanciano, Juan Carlos & Pardo-Fernandez, Juan Carlos & Van Keilegom, Ingrid, 2015. "Asymptotic distribution-free tests for semiparametric regressions," LIDAM Discussion Papers ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Joydeep Chowdhury & Probal Chaudhuri, 2020. "Convergence rates for kernel regression in infinite-dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 471-509, April.

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