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.
A Note on Density Estimation for Circular Data / Marco Di Marzio; Agnese Panzera; Charles C. Taylor. - STAMPA. - (2012), pp. 297-304. [10.1007/978-3-642-21037-2 27]
A Note on Density Estimation for Circular Data
PANZERA, AGNESE;
2012
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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