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Nonparametric estimation for a functional-circular regression model

Author

Listed:
  • Andrea Meilán-Vila

    (Universidad Carlos III de Madrid)

  • Rosa M. Crujeiras

    (Universidade de Santiago de Compostela)

  • Mario Francisco-Fernández

    (Universidade da Coruña. CITIC)

Abstract

Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should present a mild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response) would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya–Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves.

Suggested Citation

  • Andrea Meilán-Vila & Rosa M. Crujeiras & Mario Francisco-Fernández, 2024. "Nonparametric estimation for a functional-circular regression model," Statistical Papers, Springer, vol. 65(2), pages 945-974, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01420-5
    DOI: 10.1007/s00362-023-01420-5
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. Peter D. Howe, 2018. "Perceptions of seasonal weather are linked to beliefs about global climate change: evidence from Norway," Climatic Change, Springer, vol. 148(4), pages 467-480, June.
    3. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    5. Antoniadis, Anestis & Sapatinas, Theofanis, 2007. "Estimation and inference in functional mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4793-4813, June.
    6. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    7. Andrea Taylor & Wändi Bruine de Bruin & Suraje Dessai, 2014. "Climate Change Beliefs and Perceptions of Weather‐Related Changes in the United Kingdom," Risk Analysis, John Wiley & Sons, vol. 34(11), pages 1995-2004, November.
    8. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, June.
    9. Germán Aneiros‐Pérez & Ricardo Cao & Juan M. Vilar‐Fernández, 2011. "Functional methods for time series prediction: a nonparametric approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 377-392, July.
    10. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    11. Macro Di Marzio & Agnese Panzera & Charles C. Taylor, 2012. "Non-parametric smoothing and prediction for nonlinear circular time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(4), pages 620-630, July.
    12. Nengxiang Ling & Lingyu Wang & Philippe Vieu, 2020. "Convergence rate of kernel regression estimation for time series data when both response and covariate are functional," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 713-732, August.
    13. Davide Buttarazzi & Giuseppe Pandolfo & Giovanni C. Porzio, 2018. "A boxplot for circular data," Biometrics, The International Biometric Society, vol. 74(4), pages 1492-1501, December.
    14. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    15. Th. Gasser & P. Hall & B. Presnell, 1998. "Nonparametric estimation of the mode of a distribution of random curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 681-691.
    16. Nengxiang Ling & Shuyu Meng & Philippe Vieu, 2019. "Uniform consistency rate of kNN regression estimation for functional time series data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(2), pages 451-468, April.
    17. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    18. F Ferraty & S NAGY, 2022. "Scalar-on-function local linear regression and beyond [Cross-validated estimations in the single-functional index model]," Biometrika, Biometrika Trust, vol. 109(2), pages 439-455.
    19. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
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