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线性过程误差下概率密度函数核估计的均方相合性 总被引:2,自引:0,他引:2
凌能祥 《纯粹数学与应用数学》2004,20(2):99-102
设{Xt,t≥1}为一单边线性平稳过程序列,具有共同的未知密度函数f(x),本文定义通常的f(x)的核估计,在适当条件下,证明了其均方相合性. 相似文献
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设{Xt,t≥0}为定义在R^d上的随机过程,它由模型Xt=zt Φ(Yt) εt确定,{Yt}和{εt}相互独立,而zt为非随机变量,对于连续观察的样本,本文给出了非参数密度核估计极其在均方意义下的最优收敛速度,并讨论了非随机项运动形式对此速度的影响。 相似文献
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本文提出了利用一维核函数构造多维密度函数一个新估计的方法.首先利用球极投影变换将具有密度f(x),X∈Rd的样本变换为具有密度g(y),y∈Ωd 1={y:y∈Rd 1,‖y‖=1)的样本.其次,建立f与g的关系.最后,利用球面数据密度核估计构造f的一个新估计f^n.在核K及密度f(x)满足一定条件(见§1定理1.1)下,获得了f^n到,的逐点强收敛速度. 相似文献
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本文提出了利用一维核函数构造多维密度函数一个新估计的方法.首先利用球极投影变换将具有密度f(x),x∈Rd的样本变换为具有密度g(y),y∈Ωd+1={yy∈Rd+1,‖y‖=1}的样本.其次,建立f与g的关系.最后,利用球面数据密度核估计构造f的一个新估计fn.在核K及密度f(x)满足一定条件(见§1定理1.1)下,获得了(f∧)n到f的逐点强收敛速度. 相似文献
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本文用[1]发展的计数过程去研究截断样本下强率函数核估计的渐进正态性.在弱于[7]和[10]的条件下,得到了更一般的结果.接着我们将这种方法运用到密度函数核估计,在较弱的条件下,得到了截断样本下密度函数核估计的渐进正态性. 相似文献
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鲍玉芳 《数学物理学报(A辑)》1999,19(1):94-100
证明了分支特征为ψ(z)=z^2,底过程为d≤3的暂留Ornstein-Uhlenbeck(O.U.)过程的超过程Xt的占位时过程Y(t)=∫^t0Xsds关于Lebesgue测度绝对连续,且其密度过程Y(t,x)关于t≥0,x∈R^d联合连续。 相似文献
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B值平稳线性过程的迭对数律及随机指标中心极限定理 总被引:1,自引:0,他引:1
杨小云 《数学年刊A辑(中文版)》1996,(6)
设 { εt;t∈Z}是独立同分布的 B值随机元序列 ,aj;j∈ Z是一实数序列 ,并且 ∞j=-∞| aj| <∞ ,定义平稳线性过程 Xt= ∞j=-∞ajεt- j.本文研究 { Xt;t∈ IN }部分和序列的收敛性质和极限定理 ,给出了 { Xt;t∈ IN }满足有界迭对数律、紧迭对数律及随机指标中心极限定理的充分条件 相似文献
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二参数Ornstein-Uhlenbeck过程最大值分布估计 总被引:1,自引:0,他引:1
本文研究二参数 Ornstein-Uhlenbeck 过程 X(t),t∈R~2的极大值问题,得到了 Pr{max(X(t),t∈[0,T])>y}上、下界的一个估计式与 Pr{max(x(t),t∈D)>y}的渐近公式,其中 D 是 R~2中的有界 Lebesgue 可测集. 相似文献
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本文在α-混合严平稳过程的假设下,研究了条件概率密度核估计的偏和均方误差.在此基础上给出了核估计的渐近最优带宽,并以S&P500指数为例展示了本文的结果. 相似文献
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Rob J. Hyndman David M. Bashtannyk Gary K. Grunwald 《Journal of computational and graphical statistics》2013,22(4):315-336
Abstract We consider the kernel estimator of conditional density and derive its asymptotic bias, variance, and mean-square error. Optimal bandwidths (with respect to integrated mean-square error) are found and it is shown that the convergence rate of the density estimator is order n –2/3. We also note that the conditional mean function obtained from the estimator is equivalent to a kernel smoother. Given the undesirable bias properties of kernel smoothers, we seek a modified conditional density estimator that has mean equivalent to some other nonparametric regression smoother with better bias properties. It is also shown that our modified estimator has smaller mean square error than the standard estimator in some commonly occurring situations. Finally, three graphical methods for visualizing conditional density estimators are discussed and applied to a data set consisting of maximum daily temperatures in Melbourne, Australia. 相似文献
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This Note focuses on an estimator of the conditional mode of a scalar response Y given a functional random variable X. We start by building a kernel estimator of the conditional density of Y given X; the conditional mode is defined as the value which maximizes this conditional density. We establish the almost complete convergence for this estimate under α-mixing assumption. To cite this article: F. Ferraty et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Castellana and Leadbetter (1986) have shown that local irregularity of observed sample paths introduces further information which allows nonparametric estimators to reach parametric rates in mean square. In particular, the kernel density estimator fT associated with the observed sample path (Xt, t ∈[0, T]), under suitable conditions, converges in mean square to f, the unknown marginal density of the stationary process (Xt). So it seems natural to ask a question: can we also estimate the density's derivative with a parametric rate?
相似文献15.
In this paper moving-average processes with no parametric assumption on the error distribution are considered. A new convolution-type estimator of the marginal density of a MA(1) is presented. This estimator is closely related to some previous ones used to estimate the integrated squared density and has a structure similar to the ordinary kernel density estimator. For second-order kernels, the rate of convergence of this new estimator is investigated and the rate of the optimal bandwidth obtained. Under limit conditions on the smoothing parameter the convolution-type estimator is proved to be
-consistent, which contrasts with the asymptotic behavior of the ordinary kernel density estimator, that is only
-consistent. 相似文献
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Toshio Honda 《Annals of the Institute of Statistical Mathematics》2000,52(4):599-611
We estimate the marginal density function of a long-range dependent linear process by the kernel estimator. We assume the innovations are i.i.d. Then it is known that the term of the sample mean is dominant in the MISE of the kernel density estimator when the dependence is beyond some level which depends on the bandwidth and that the MISE has asymptotically the same form as for i.i.d. observations when the dependence is below the level. We call the latter the case where the dependence is not very strong and focus on it in this paper. We show that the asymptotic distribution of the kernel density estimator is the same as for i.i.d. observations and the effect of long-range dependence does not appear. In addition we describe some results for weakly dependent linear processes. 相似文献
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研究了条件泛函及其导数的非参数估计,对随机与固定设计的条件泛函,分别利用核估计和非参数加权估计,在核函数及权函数满足一定条件下,证明了估计一致强收敛于待估函数的速度可达到最优。从而进一步推广和发展了Hrdle,etal.(1988)、Severini,etal.(1992)的许多结果。 相似文献
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Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are derived.Secondly,the corresponding strong convergence rates are investigated.It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d.density models are also optimal for these processes. 相似文献
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XueLiugen CaiGuoliang 《高校应用数学学报(英文版)》2000,15(4):425-432
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y!|x) are studied. The results may be used to construct the confidence interval of f(y|x). 相似文献
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Xue Liugen Cai GuoliangDept.of Appl.Math. Beijing Polytechnic Univ. Beijing . Faculty of Science Jiangsu Univ.of Science Technology Zhenjiang . 《高校应用数学学报(英文版)》2000,(4)
§ 1 IntroductionLet(X,Y) be a random vector taking values Rp×Rqand assume that with given X=x,f(y|x) is the conditional density of Y,the Borel-measurable function on(x,y) ,X has amarginal distribution function F(x) and a marginal density function f(x) .Let(X1 ,Y1 ) ,...,(Xn,Yn) be i.i.d.sample taking values in(X,Y) .A class of double kernel esti-mates of f(y|x) proposed by Zhao Linchang and Liu Zhijun[1 ] has the formfn(y|x) = ni=1K1Xi -xan K2Yi -ybn bqn nj=1K1Xj-xan ,(1 .1 )where… 相似文献