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Wavelet estimation in varying-coefficient partially linear regression models

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  • Zhou, Xian
  • You, Jinhong

Abstract

This paper is concerned with the estimation of a varying-coefficient partially linear regression model that is frequently used in statistical modeling. We first construct estimators of the parametric components and the error variance by a wavelet procedure and establish their asymptotic normalities under weaker conditions than those assumed in the previous literature. Then we propose appropriate estimators for the functions characterizing the nonlinear part of the model and derive their convergence rates. Furthermore, we present consistent estimators for the asymptotic (co)variances of the parametric components and error variance estimators as well. These results can be used to make asymptotically valid statistical inference.

Suggested Citation

  • Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:91-104
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    References listed on IDEAS

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    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    2. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
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    Cited by:

    1. Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    2. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    3. Shuanghua Luo & Yuxin Yan & Cheng-yi Zhang, 2024. "Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
    4. Hong-Xia Xu & Guo-Liang Fan & Han-Ying Liang, 2024. "Quantile regression for varying-coefficient partially nonlinear models with randomly truncated data," Statistical Papers, Springer, vol. 65(4), pages 2567-2604, June.
    5. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    6. Zhou, Xing-cai & Xu, Ying-zhi & Lin, Jin-guan, 2017. "Wavelet estimation in varying coefficient models for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 179-189.
    7. Weiwei Zhang & Jingxuan Luo & Shengyun Ma, 2023. "Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses," Mathematics, MDPI, vol. 11(23), pages 1-20, December.
    8. Fen Li & Hao Chen & Bogui Li, 2026. "Estimation of random effects partially linear varying coefficient spatial error model with general temporally correlated individuals," Statistical Papers, Springer, vol. 67(2), pages 1-38, April.
    9. Li, Yongming & Yang, Shanchao & Zhou, Yong, 2008. "Consistency and uniformly asymptotic normality of wavelet estimator in regression model with associated samples," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2947-2956, December.
    10. Zhang, Weiwei & Li, Gaorong & Xue, Liugen, 2011. "Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3027-3040, November.
    11. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
    12. Xingcai Zhou & Guang Yang & Yu Xiang, 2022. "Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models," Mathematics, MDPI, vol. 10(13), pages 1-15, July.

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