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A plug-in the number of knots selector for polynomial spline regression

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  • Shujie Ma

Abstract

A plug-in the number of interior knots (NIKs) selector is proposed for polynomial spline estimation in nonparametric regression. The existence and properties of the optimal NIKs for spline regression are established by minimising the weighted mean integrated squared error. We obtain plug-in formulae for the optimal NIKs based on the theoretical results of asymptotic optimality, and develop strategies for choosing the NIKs of the spline estimator. The proposed NIKs selection method is tested on our simulated data with quite satisfactory performance, and is illustrated by analysing a fossil data set.

Suggested Citation

  • Shujie Ma, 2014. "A plug-in the number of knots selector for polynomial spline regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 489-507, September.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:489-507
    DOI: 10.1080/10485252.2014.930143
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    Cited by:

    1. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    2. Kristy P. Robledo & Ian C. Marschner, 2021. "A new algorithm for fitting semi-parametric variance regression models," Computational Statistics, Springer, vol. 36(4), pages 2313-2335, December.
    3. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.
    5. Zhong, Chen, 2024. "Oracle-efficient estimation and trend inference in non-stationary time series with trend and heteroscedastic ARMA error," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).

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