Comparison of relative efficiency of kernel density estimator with the exponential map

• Published in: Journal of the Korean Statistical Society Vol. 42; no. 2; pp. 267 - 275
• Main Author: Park, Hyun Suk
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.06.2013; Springer Singapore; 한국통계학회
• Subjects: [formula omitted]-minimax rate; Applied Statistics; Bayesian Inference; Exponential map; Kernel density estimator; Relative efficiency; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; 62G20; Exponential map; Kernel density estimator; 62G07; L2-minimax rate; Relative efficiency; minimax rate; L
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2012.08.007

This paper considers the relative efficiency of two kernel estimators which have been proposed by Park [Park, H.S. (2012). Asymptotic behavior of the kernel density estimator from a geometric viewpoint. Communications in Statistics. Theory and Methods, 41(19),3479–3496.] and Hall et al. [Hall, P., Watson, G., & Cabrera, J. (1987). Kernel density estimation with spherical data. Biometrika, 74, 751-762.], respectively. For this, we first consider the L2-minimax rate of the estimator defined by the exponential map. In order to make a numerical study between these estimators, the computing flows for the relative efficiency are introduced on the 2-dimensional unit sphere. A comparison between the two estimators with two different kernels is also investigated.