φ-混合随机域频率插值估计
发布时间：2018-12-19 21:17
【摘要】：非参数密度估计是一类重要的密度估计,它在实际生活中有着广泛的应用.在自然界中,大多数总体还是未知分布以及样本不一定是独立的,所以非参数密度函数估计的问题在数理统计的研究中备受关注.非参数密度函数的估计从最初的直方图密度估计,经过不断地探索逐步有了Rosenblatt密度估计、Parzen核估计、核密度估计、最近邻密度估计、移动平均直方图密度估计和频率插值密度估计等等.1985年Scott[5]在直方图估计的基础上提出了频率插值密度估计,并指出:选择最优窗宽使均方误差最小下,得到的收敛速度分别为:n-2/3和n-4/5,同时,φ混合序列在时间序列模型、可靠性理论、生态系统研究等领域具有广泛的应用,因此统计学家对φ混合序列的研究有着广泛关注和兴趣.Scott(1985)[5]提出频率插值密度估计,很多学者做出深入研究.然而,目前还没有文献对φ混合随机域该估计的性质进行更多的研究.因此,在φ-混合随机域下对频率插值密度估计渐近性质的研究是有意义的.本文在φ-混合随机域下,主要是对频率插值密度估计渐近性质的研究.首先,介绍φ-混合、频率插值密度估计.其次,混合系数φ满足∑i=1∞iN-1(φ(i))β∞,其中0β1.证明出limn→∞(nbnVarfn(x)-[1/2 + 2(k0-x/bn)f(x))= 0.借助Carbona(2010)等对α-随机域里频率多边形采用“大小分块”的思想,对φ-混合随机域大小分块,来证明φ-混合样本下频率插值的渐近正态性.
[Abstract]:Nonparametric density estimation is an important class of density estimation, which is widely used in real life. In nature, most of the population is unknown and the samples are not necessarily independent, so the problem of nonparametric density function estimation has attracted much attention in the research of mathematical statistics. The estimation of nonparametric density function from the original histogram density estimation, after continuous exploration, there are gradually Rosenblatt density estimation, Parzen kernel estimation, kernel density estimation, nearest neighbor density estimation. Moving average histogram density estimation and frequency interpolation density estimation, etc. In 1985, Scott [5] proposed a frequency interpolation density estimation based on histogram estimation, and pointed out that when the optimal window width is chosen to minimize the mean square error, The convergence rates obtained are n-2 / 3 and n-4 / 5, respectively. Meanwhile, 蠁 mixed sequences are widely used in time series model, reliability theory, ecosystem research and so on. Therefore, statisticians have a wide range of concerns and interests in the study of 蠁 mixed sequences. [5] [5] Frequency interpolation density estimation has been proposed by many scholars. However, there are no more studies on the properties of this estimator in 蠁 mixed random fields. Therefore, it is significant to study the asymptotic properties of frequency interpolation density estimation in 蠁-mixed random field. In this paper, the asymptotic properties of density estimation of frequency interpolation in 蠁-mixed random domain are studied. Firstly, 蠁-mixing and frequency interpolation density estimation are introduced. Secondly, the mixing coefficient 蠁 satisfies 鈭，
本文编号：2387476
[Abstract]:Nonparametric density estimation is an important class of density estimation, which is widely used in real life. In nature, most of the population is unknown and the samples are not necessarily independent, so the problem of nonparametric density function estimation has attracted much attention in the research of mathematical statistics. The estimation of nonparametric density function from the original histogram density estimation, after continuous exploration, there are gradually Rosenblatt density estimation, Parzen kernel estimation, kernel density estimation, nearest neighbor density estimation. Moving average histogram density estimation and frequency interpolation density estimation, etc. In 1985, Scott [5] proposed a frequency interpolation density estimation based on histogram estimation, and pointed out that when the optimal window width is chosen to minimize the mean square error, The convergence rates obtained are n-2 / 3 and n-4 / 5, respectively. Meanwhile, 蠁 mixed sequences are widely used in time series model, reliability theory, ecosystem research and so on. Therefore, statisticians have a wide range of concerns and interests in the study of 蠁 mixed sequences. [5] [5] Frequency interpolation density estimation has been proposed by many scholars. However, there are no more studies on the properties of this estimator in 蠁 mixed random fields. Therefore, it is significant to study the asymptotic properties of frequency interpolation density estimation in 蠁-mixed random field. In this paper, the asymptotic properties of density estimation of frequency interpolation in 蠁-mixed random domain are studied. Firstly, 蠁-mixing and frequency interpolation density estimation are introduced. Secondly, the mixing coefficient 蠁 satisfies 鈭，
本文编号：2387476
本文链接：https://www.wllwen.com/kejilunwen/yysx/2387476.html
