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Local polynomial regression for circular predictors

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  • Di Marzio, Marco
  • Panzera, Agnese
  • Taylor, Charles C.

Abstract

We consider local smoothing of datasets where the design space is the d-dimensional (d>=1) torus and the response variable is real-valued. Our purpose is to extend least squares local polynomial fitting to this situation. We give both theoretical and empirical results.

Suggested Citation

  • Di Marzio, Marco & Panzera, Agnese & Taylor, Charles C., 2009. "Local polynomial regression for circular predictors," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2066-2075, October.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:2066-2075
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    References listed on IDEAS

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    1. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    2. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    3. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    4. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
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    Cited by:

    1. Oliveira, María & Crujeiras, Rosa M. & Rodríguez-Casal, Alberto, 2014. "NPCirc: An R Package for Nonparametric Circular Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i09).
    2. 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.
    3. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    4. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    5. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    6. Eduardo GarcÍa-Portugués & Ingrid Van Keilegom & Rosa M. Crujeiras and & Wenceslao González-Manteiga, 2016. "Testing parametric models in linear-directional regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1178-1191, December.
    7. Marco Di Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2022. "Density estimation for circular data observed with errors," Biometrics, The International Biometric Society, vol. 78(1), pages 248-260, March.
    8. Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.
    9. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Local binary regression with spherical predictors," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 30-36.
    10. Zihao Wu & Carolina Euan & Rosa M. Crujeiras & Ying Sun, 2023. "Estimation and Clustering of Directional Wave Spectra," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 502-525, September.
    11. Bedouhene Kahina & Zougab Nabil, 2020. "A Bayesian procedure for bandwidth selection in circular kernel density estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 69-82, March.
    12. Said Benlakhdar & Mohammed Rziza & Rachid Oulad Haj Thami, 2022. "Statistical modeling of directional data using a robust hierarchical von mises distribution model: perspectives for wind energy," Computational Statistics, Springer, vol. 37(4), pages 1599-1619, September.

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