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- 2017
WOD样本下密度函数核估计的收敛性
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Abstract:
摘要： 设{Xn,n≥1}为同分布的WOD随机序列, f(x)为共同的概率密度函数。利用WOD序列的Rosenthal-型矩不等式和Bernstein-型指数不等式, 对密度函数f(x)的核估计进行了探讨, 在适当条件下得到了核估计的r 阶相合性、逐点强相合性和依概率一致收敛性。
Abstract: Let {Xn,n≥1} be an identically distributed WOD random sequence with a commen density functiong f(x). Based on the Rosenthal-type inequality and Bernstein-type inequality for WOD sequence, the kernel estimator for density function f(x)was investigated under suitable conditions, and the consistency in r order mean, the pointwise strong consistency and uniform consistency in L1 were obtained
| [1] | 韦来生. NA样本概率密度函数核估计的相合性[J]. 系统科学与数学, 2001, 21(1): 79-87. WEI Laisheng. The consistencies for the kernel-type density estimation in the case of NA samples[J]. Journal of System Science and Mathematical Science, 2001, 21(1): 79-87. |
| [2] | 刘永辉,吴群英.ND样本最近邻密度估计的相合性[J].吉林大学学报(理学版), 2012,50(6):1141-1145. LIU Yonghui, WU Qunying. Consistency of nearest neighbor estimator of density function for ND samples[J]. Journal of Jilin University(Science Edition), 2012, 50(6): 1141-1145. |
| [3] | SHEN Anting. Bernstein-type inequality for widely dependent sequence and its application to non-parametric regression models[J]. Abstract and Applied Analysis, 2013(1): 309-338. |
| [4] | JOAG-DEV K, PROSCHAN F. Negative association of random variables with applications[J]. Annals of Statistics, 1983, 11: 286-295. |
| [5] | LIU Li. Precise large deviations for dependent random variables with heavy tails[J]. Statistics and Probability Letters, 2009, 79(9):1290-1298. |
| [6] | 李永明, 应锐, 蔡际盼,等. WOD 样本密度函数和失效率函数递归核估计的逐点强相合性[J]. 吉林大学学报(理学版), 2015, 53(6): 1134-1138. LI Yongming, YING Rui, CAI Jipan, et al. Pointwise strong consistency of recursive kernel estimator for probability density and failure rate funciton under WOD sequence[J]. Journal of Jilin University(Science Edition), 2015, 53(6): 1134-1138. |
| [7] | WANG Xuejun, XU Chen, HU Tienchung, et al. On complete convergence for widely orthant dependent random variables and its applications in nonparametric regression models[J]. TEST, 2014, 23(3): 607-629. |
| [8] | CHUNG K L. A course in probability theory[M]. New York: Academic Press, 1974. |
| [9] | WANG Kaiyong, WANG Yuebao, GAO Qingwu. Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate[J]. Methodology and Computing in Applied Probability, 2013, 15(1): 109-124. |
| [10] | ROSENBLATT M. Remarks on some nonparametric estimates of a density function[J]. The Annals of Mathematical Statistics, 1956, 27(3): 832-837. |
| [11] | PARZEN E. On estimation of a probability density function and mode[J]. The Annals of Mathematical Statistics, 1962, 33: 1065-1076. |
| [12] | 陈希孺, 方兆本, 李国英,等. 非参数统计[M]. 上海:上海科技出版社, 1989. CHEN Xiru, FANG Zhaoben, LI Guoying, et al. Nonparametric statistics[M]. Shang Hai: Shang Hai Science and Technology Press, 1989. |
