Abstract
We discuss kernel density estimation for data lying on the d-dimensional torus (d ≥ 1). We consider a specific class of product kernels, and formulate exact and asymptotic L 2 properties for the estimators equipped with these kernels. We also obtain the optimal smoothing for the case when the kernel is defined by the product of von Mises densities. A brief simulation study illustrates the main findings.
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Di Marzio, M., Panzera, A., Taylor, C.C. (2012). A Note on Density Estimation for Circular Data. In: Di Ciaccio, A., Coli, M., Angulo Ibanez, J. (eds) Advanced Statistical Methods for the Analysis of Large Data-Sets. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21037-2_27
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DOI: https://doi.org/10.1007/978-3-642-21037-2_27
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