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Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates

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  • Li, Degui
  • Lu, Zudi
  • Linton, Oliver

Abstract

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

Suggested Citation

  • Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(5), pages 935-958, October.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:05:p:935-958_00
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    References listed on IDEAS

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    Cited by:

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    2. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    4. Jia Chen & Degui Li & Oliver Linton & Zudi Lu, 2015. "Semiparametric model averaging of ultra-high dimensional time series," CeMMAP working papers CWP62/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Chen, Jia & Li, Degui & Linton, Oliver & Lu, Zudi, 2016. "Semiparametric dynamic portfolio choice with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 194(2), pages 309-318.
    6. Degui Li & Oliver Linton & Zudi Lu, 2012. "A Flexible Semiparametric Model for Time Series," Monash Econometrics and Business Statistics Working Papers 17/12, Monash University, Department of Econometrics and Business Statistics.
    7. Botosaru, Irene & Sasaki, Yuya, 2018. "Nonparametric heteroskedasticity in persistent panel processes: An application to earnings dynamics," Journal of Econometrics, Elsevier, vol. 203(2), pages 283-296.
    8. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    9. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    10. Yang, Lixiong & Lee, Chingnun & Shie, Fu Shuen, 2014. "How close a relationship does a capital market have with other markets? A reexamination based on the equal variance test," Pacific-Basin Finance Journal, Elsevier, vol. 26(C), pages 198-226.
    11. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    12. Lee, Jiyon, 2015. "A semiparametric single index model with heterogeneous impacts on an unobserved variable," Journal of Econometrics, Elsevier, vol. 184(1), pages 13-36.
    13. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    14. James A. Duffy, 2015. "Uniform Convergence Rates over Maximal Domains in Structural Nonparametric Cointegrating Regression," Economics Papers 2015-W03, Economics Group, Nuffield College, University of Oxford.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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