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A nonparametric circular-linear multivariate regression model with a rule-of-thumb bandwidth selector. (English) Zbl 1232.62067

Summary: The purpose of this paper is to propose a nonparametric circular-linear multivariate regression model using a kernel-weighted local linear method. The case of several linear regressors and one circular regressor is considered. We extend results on the asymptotic bias and variance of the linear multivariate variable to the case of circular-linear multivariate variables. The rule-of-thumb selector is used to establish the optimal bandwidths for the nonparametric model. The suitability of the model is judged from the coefficient of determination. A simulation experiment and a real problem concerning wind energy are used to study the power performance of the nonparametric model.

MSC:

62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
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References:

[1] SenGupta, A.; Ugwuowo, F. I., Asymmetric circular-linear multivariate regression models with applications to environmental data, Environmental and Ecological Statistics, 13, 299-309 (2006)
[2] Justus, C. G., Winds and Wind System Performance (1978), The Franklin Institute Press: The Franklin Institute Press Philadelphia
[3] Jammalamadaka, S. R.; SenGupta, A., Tropic in Circular Statistics (2001), World Scientific Publishing
[4] Johnson, R. A.; Wehrly, T. E., Some angular-linear distributions and related regression models, Journal of the American Statistical Association, 73, 602-606 (1978) · Zbl 0388.62059
[5] SenGupta, A., On the constructions of probability distributions for directional data, Bulletin of the Indian Mathematical Society, 96, 139-154 (2004) · Zbl 1052.62061
[6] Bhattacharya, S.; SenGupta, A., Bayesian analysis of semiparametric linear-circular models, Journal of Agricultural, Biological, and Environmental Statistics, 14, 33-65 (2009) · Zbl 1306.62245
[7] Ruppert, D.; Wand, M. P., Multivariate locally weighted least squares regression, The Annals of Statistics, 3, 1346-1370 (1994) · Zbl 0821.62020
[8] Härdle, W.; Müller, Marlene; Sperlich, Stefan, Nonparametric and Semiparametric Models (2004), Springer: Springer Berlin · Zbl 1059.62032
[9] Marzio, M. D.; Panzera, A.; Taylor, C. C., Local polynomial regression for circular predictors, Statistics and Probability Letters, 79, 2066-2075 (2009) · Zbl 1171.62327
[10] Yang, L. J.; Tschernig, R., Multivariate bandwidth selection for local linear regression, Journal of the Royal Statistical Society, 61, 793-815 (1999) · Zbl 0952.62039
[11] Ruppert, D.; Sheather, S. J.; Wand, M. P., An effective bandwidth selector for local least squares regression, Journal of the American Statistical Association, 90, 1257-1270 (1995) · Zbl 0868.62034
[12] Fan, J.; Gijbels, I., Adaptive order polynomial fitting: bandwidth robustification and bias reduction, Journal of Computational and Graphical Statistics, 4, 213-227 (1995)
[13] Li, Q.; Racine, J. S., Nonparametric Econometrics: Theory and Practice (2007), Princeton University Press: Princeton University Press Princeton · Zbl 1183.62200
[14] Marzio, M. D.; Panzera, A.; Taylor, C. C., Kernel density estimation on the torus, Journal of Statistical Planning and Inference, 141, 2156-2173 (2011) · Zbl 1208.62065
[15] Li, Q.; Racine, J., Cross-validated local linear nonparametric regression, Statistica Sinica, 14, 485-512 (2004) · Zbl 1045.62033
[16] Y.A. Cengel, M.A. Boles, in: Thermodynamics—An Engineering Approach, McGraw-Hill Series in Mechanical Engineering, 3rd ed., Boston, 1998.; Y.A. Cengel, M.A. Boles, in: Thermodynamics—An Engineering Approach, McGraw-Hill Series in Mechanical Engineering, 3rd ed., Boston, 1998.
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