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Ӧ�ø��ͳ�� 2015, 31(3) 238-246 DOI: ISSN: 1001-4268 CN: 31-1256

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�� $\100dpi \inline $f_n$$ �ǻ��һ��˺�� $\100dpi \inline $K$$ ��ȡֵ�� $\100dpi \inline $\mathbb{R}^d$$ �Ķ��
ͬ�ֲ��е�һ��ǲ��ܶȹ��. ��ƹ��He��Gao(2008)��Ӧ��ƫ��Ľ��,
��֤��ͳ�� $\100dpi \inline $\sup\limits_{x\in\mathbb{R}^d}|f_n(x)-f_n(-x)|$$ �Ĵ�ƫ��.

�ؼ���� ԳƼ�� ܶȹ�� ƫ��.

Large Deviations for a Test of Symmetry based on Kernel Density Estimator in R^d

Xu Mingzhou, Zhou Yongzheng

School of Information and Engineering, Jingdezhen Ceramic Institute

Abstract:

Let $\100dpi \inline $f_n$$ be a non-parametric kernel density estimator based
on a kernel function $\100dpi \inline $K$$ and a sequence of independent and identically distributed
random variables taking values in $\100dpi \inline $\mathbb{R}^d$$ . The goal of this article is to extend
the large deviations results in He and Gao (2008), i.e., to prove large deviations for
the statistic $\100dpi \inline $\sup\limits_{x\in\mathbb{R}^d}|f_n(x)-f_n(-x)|$$ .

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