Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data
Received:October 19, 2020  Revised:May 20, 2021
Key Word: symmetry test   kernel density estimator   directional data   large deviations  
Fund ProjectL:Supported by the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University (Grant No.102/01003002031), Program of Department of Education of Jiangxi Province of China (Grant Nos.GJJ190732; GJJ180737) and the Natural Science Foundation Program of Jiangxi Province (Grant No.20202BABL211005).
Author NameAffiliation
Mingzhou XU School of Information Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China 
Kun CHENG School of Information Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China 
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Abstract:
      Assume that $f_n$ is the nonparametric kernel density estimator of directional data based on a kernel function $K$ and a sequence of independent and identically distributed random variables taking values in $d$-dimensional unit sphere ${\mathbb{S}}^{d-1}$. We established that the large deviation principle for $\{\sup_{x\in {\mathbb{S}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$ holds if the kernel function is a function with bounded variation, and the density function $f$ of the random variables is continuous and symmetric.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.06.008
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