Journal of Jilin University Science Edition ›› 2019, Vol. 57 ›› Issue (04): 833-838.
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GUAN Lihong, XIAO Yushan, ZHAO Yanan
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Abstract: Let {Xn, n≥1} be an m-widely orthant dependence (m-WOD) sequence with the same distribution, fn(x) and rn(x) were the kernel estimators of the density function f(x) and the failure rate function based on the sample X1,X2,…,Xn, respectively. Under some suitable assumptions, we proved the strong consistency and the uniform strong consistency of the kernel density estimator and failure rate function kernel estimator by using the moment inequality for m-WOD sequence and BorelCantelli lemma.
Key words: m-WOD sequence, kernel estimator, failure rate function, (uniform) strong consistency
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GUAN Lihong, XIAO Yushan, ZHAO Yanan. Strong Consistency of Kernel Estimator of Density Functionand Failure Rate Function for m-WOD Sequence#br#[J].Journal of Jilin University Science Edition, 2019, 57(04): 833-838.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2019/V57/I04/833
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