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Estimation and testing for partially functional linear errors-in-variables models

Author

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  • Zhu, Hanbing
  • Zhang, Riquan
  • Yu, Zhou
  • Lian, Heng
  • Liu, Yanghui

Abstract

This paper considers estimation and testing problems for partial functional linear models when the covariates in the non-functional linear component are measured with additive error. A corrected profile, least-squares based, estimation procedure is developed for the parametric component. Asymptotic properties of the proposed estimators are established under some regularity conditions. To test a hypothesis on the parametric component, a statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses is proposed; its limiting null distribution is shown to be a weighted sum of independent standard χ12 variables. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for illustration.

Suggested Citation

  • Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    • Handle: RePEc:eee:jmvana:v:170:y:2019:i:c:p:296-314
    DOI: 10.1016/j.jmva.2018.11.005
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    as
    1. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    2. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    3. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    4. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    5. Comte, Fabienne & Johannes, Jan, 2012. "Adaptive functional linear regression," LIDAM Reprints ISBA 2012031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
    7. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    8. Hua Liang, 2009. "Generalized partially linear mixed-effects models incorporating mismeasured covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 27-46, March.
    9. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    10. Hongxiao Zhu & Philip J. Brown & Jeffrey S. Morris, 2012. "Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models," Biometrics, The International Biometric Society, vol. 68(4), pages 1260-1268, December.
    11. P. Z. Hadjipantelis & J. A. D. Aston & H. G. Müller & J. P. Evans, 2015. "Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 545-559, June.
    12. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    13. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    14. Ying Lu & Jiang Du & Zhimeng Sun, 2014. "Functional partially linear quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 317-332, February.
    15. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    16. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    17. Daowen Zhang & Xihong Lin & MaryFran Sowers, 2007. "Two-Stage Functional Mixed Models for Evaluating the Effect of Longitudinal Covariate Profiles on a Scalar Outcome," Biometrics, The International Biometric Society, vol. 63(2), pages 351-362, June.
    18. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    19. Li, Yehua & Hsing, Tailen, 2007. "On rates of convergence in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1782-1804, October.
    20. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    21. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    22. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    23. Germán Aneiros-Pérez & Philippe Vieu, 2013. "Testing linearity in semi-parametric functional data analysis," Computational Statistics, Springer, vol. 28(2), pages 413-434, April.
    24. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    25. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    26. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    27. Yehua Li & Naisyin Wang & Raymond J. Carroll, 2013. "Selecting the Number of Principal Components in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1284-1294, December.
    28. Shin, Hyejin & Lee, Myung Hee, 2012. "On prediction rate in partial functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 93-106, January.
    29. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    30. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
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    2. Belli, Edoardo, 2022. "Smoothly adaptively centered ridge estimator," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Zhu, Hanbing & Zhang, Yuanyuan & Li, Yehua & Lian, Heng, 2023. "Semiparametric function-on-function quantile regression model with dynamic single-index interactions," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. Římalová, Veronika & Fišerová, Eva & Menafoglio, Alessandra & Pini, Alessia, 2022. "Inference for spatial regression models with functional response using a permutational approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    6. Yu, Ping & Song, Xinyuan & Du, Jiang, 2024. "Composite expectile estimation in partial functional linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    7. Fanrong Zhao & Baoxue Zhang, 2024. "A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model," Mathematics, MDPI, vol. 12(16), pages 1-23, August.

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