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1.
周勇 《数学学报》1997,40(4):603-614
设平稳序列   其共同分布为F。本文研究了β-混合和α-混合序列的经验过程增量,在混合速度为非指数速度的情况下给出了经验过程增量的强收敛和弱收敛意义下的收敛速度,在分布函数F绝对连续时,构造了核光滑经验分布函数估计,并利用经验过程增量的收敛速度建立了该光滑经验分布函数逼近及真分布函数的收敛速度。  相似文献   

2.
本文中, Owen 引入的经验似然方法被用于参数空间带不等式约束的两总体中位数的比较. 迄今为止, 还没有人研究过该问题. 这是因为, 在构造经验似然函数过程中所使用的辅助函数不是光滑函数, 因而不是凸函数, 从而使研究难度大大增加. 然而, 通过引入经验过程的办法, 本文很巧妙地解决了此问题. 根据经验过程, 本文证明了两中位数比较的经验似然比检验统计量的极限分布要么是单一的卡方分布, 要么是两个卡方分布的等权混合分布. 这一理论结果得到了模拟运算结果的有力支持.  相似文献   

3.
本文考虑与对称分布有关的经验过程的自助(Bootstrap)问题.证明了对称分布之分布函数的自助估计的相合性.同时还讨论了用自助法构造对称分布函数的置信界的方法.  相似文献   

4.
本文研究了 Chernoff-Savage 统计量的分布函数的 Bootstrap 估计问题.证明了Bootstrap 分布函数是 a.s.渐近相合的估计量.同样的结论对有关的两样本经验过程也成立.  相似文献   

5.
本文研究了Ghernoff-Savage统计量的分布函数的Bootstrap估计问题。证明了Bootstrap分布函数是a.s.渐近相台的估计量。同样的结论对有关的两样本经验过程也成立。  相似文献   

6.
关忠 《应用概率统计》1993,9(4):402-408
本文考虑与对称分布有关的经验过程的自助(Bootstrap)问题。证明了对称分布之分布函数的自助估计的相合性。同时还讨论了用自助法构造对称分布函数的置信界的方法。  相似文献   

7.
二维连续型随机变量函数的密度函数的计算既是概率论教学中的一个重点,又是一个难点.本文介绍了一般二维连续型随机变量函数的分布密度的计算方法,并给出了一个新的方法——密度函数转化法.  相似文献   

8.
常见连续型统计分布的一点注记   总被引:1,自引:0,他引:1  
正态分布是概率论与数理统计中最重要的一个分布,本文讨论了常见的连续型统计分布与标准正态分布间的关系,结果表明:几乎所有的常见连续型统计分布都是标准正态分布的函数.  相似文献   

9.
<正> 一般教材求连续型随机变量的分布函数均采用分布函数的定义来求.笔者认为这种方法在计算上有很多麻烦,但对初学者来说较难掌握,笔者经过大量的计算和总结发现可用不定积分法求连续型随机变量的分布函数,它省时省事,且较易掌握.设ξ为连续型随机变量,F(x)为ξ的分布函数,Φ(x)为ξ的分布密度函数,且  相似文献   

10.
应用积分经验过程检验多元分布函数的相等性   总被引:3,自引:0,他引:3  
景平  杨元 《应用数学》2007,20(3):614-620
本文引进投影积分经验过程用于检验两个或K个多元分布函数的相等性,自助法用于确定临界值的逼近,数论方法有效地计算自动法确定的临界值,且进行了一些模拟试验.  相似文献   

11.
Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. Illustrations are provided and consequences for inference are outlined.  相似文献   

12.
This paper considers a continuous time, continuous state stochastic process to determine a theoretical model and empirical parameters for the probability distribution of remigration. A Brownian motion model is used for simplicity, with empirical findings drawn from a study of Israeli return migrants. A negative relationship between remigration (sojourn) time and the probability of return time is used to provide forecasts of remigration which can help governments who seek actively the return of their migrants to reach better decisions regarding the timing of their efforts.  相似文献   

13.
We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.This research has been supported in part by NSF Grants ECS-8811003 and DDM-8905638.  相似文献   

14.
This paper introduces a functional central limit theorem for empirical processes endowed with real values from a strictly stationary random field that satisfies an interlaced mixing condition. We proceed by using a common technique from Billingsley (Convergence of probability measures, Wiley, New York, 1999), by first obtaining the limit theorem for the case where the random variables of the strictly stationary ???-mixing random field are uniformly distributed on the interval [0, 1]. We then generalize the result to the case where the absolutely continuous marginal distribution function is not longer uniform. In this case we show that the empirical process endowed with values from the ???-mixing stationary random field, due to the strong mixing condition, doesn??t converge in distribution to a Brownian bridge, but to a continuous Gaussian process with mean zero and the covariance given by the limit of the covariance of the empirical process. The argument for the general case holds similarly by the application of a standard variant of a result of Billingsley (1999) for the space D(???, ??).  相似文献   

15.
Summary Let R(s,t) be the empirical process of a sequence of independent random vectors with common but arbitrary distribution function. In this paper we give an almost sure approximation of R(s,t) by a Kiefer process. The result continues to hold for stationary sequences of random vectors with continuous distribution function and satisfying a strong mixing condition.Supported in part by an NSF grant  相似文献   

16.
光滑分布函数分位数估计的注记(英)   总被引:1,自引:0,他引:1  
文中通过光滑经验分布函数构造了分位数估计,建立该估计的Bahadu-强弱表示定理,并由Bahadur表示定理证明了该分估计估的重对数律和渐近正态性等深刻结果.  相似文献   

17.
关于经验分布的最优选择问题   总被引:1,自引:0,他引:1       下载免费PDF全文
本文运用统计决策知识探索了经验分布的最优选择问题. 作者借鉴风险函数的思想, 在平方损失的意义下引进平均平方距离标准, 并推导出该标准下最优新经验分布函数. 继而采用另一源于Minimax思想的最大一次距离标准, 在连续总体下对五种经验分布函数加以模拟比较分析, 得出新经验分布函数仍一致占优.  相似文献   

18.
A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypothesis and it is proved that the limit process is a continuous Gaussian process. The structure of its covariance function allows to calculate the limit distribution and it turns out that it is a function of a standard Brownian motion and so exact rejection regions can be constructed. The proposed test is asymptotically distribution free and it is consistent under any simple fixed alternative.  相似文献   

19.
We consider two Cramér–von Mises goodness-of-fit tests for hypotheses that the observed diffusion process has sign-type trend coefficient based on empirical distribution function and empirical density function. It is shown that the limit distributions of the proposed tests statistics are defined by the integral type functionals of continuous Gaussian processes. We study the behavior of these statistics under the alternative hypothesis and we prove that the tests are consistent. We provide the Karhunen-Loève expansion on \mathbbR{\mathbb{R}} of the corresponding limiting processes and we show that the eigenfunctions in these expansions have expressions in term of Bessel functions.  相似文献   

20.
A random financial price process which is developed by mechanisms of finite-range interacting biased voter model is considered in the present paper. Voter model is one of statistical physics systems as well as a continuous time Markov process, which originally represents a voter’s attitude on a particular topic, namely, voters reconsider their opinions at times distributed according to independent exponential random variables. The empirical mode decomposition method is employed to analyze the behaviors of logarithmic returns for the simulation data of the model and the two real market indexes, Shanghai Composite Index and Deutscher Aktien Index. The multifractal characteristics of the original returns and first 3 intrinsic mode functions (IMFs) after empirical mode decomposition are explored by the multifractal detrended function analysis. The instantaneous phase, amplitude probability distribution of first 4 IMFs, and the multifractal properties of instantaneous amplitude are investigated.  相似文献   

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