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独立随机序列最大值的几乎处处极限定理 总被引:1,自引:1,他引:0
本文研究了独立随机序列最大值分布的几乎必然收敛性.利用有关协方差的不等式和加权平均,获得独立随机序列最大值的几乎处处极限.将独立同分布随机序列的结论,推广了独立但不同分布的情形. 相似文献
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利用似然比构造几乎处处收敛的上鞅,结合分析方法,给出了Laplace分布的一个强极限定理。 相似文献
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本文我们给出了基于神经元网络的随机过程的条件分位数的均方收敛速度.无论是在独立同分布情况下还是在平稳混合(α-混合β-混合)的情况下,我们都给出了相应的结果.结果与基于神经元网络的回归估计的收敛速度相同.采用的技术同Zhang(1998)一致. 相似文献
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In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this
purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic
test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is ω
2-distribution. The ω
2-distribution is only known for special cases, thus we have considered random LR-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there
is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem
for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable.
Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful
tool in the statistical hypothesis testing about the mean of fuzzy random variables. 相似文献
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A limit theorem with bounds on the rate of convergence is proven. The joint distribution of a fixed number of relative decrements
of the top order statistics from a random sample converges to the limit as the sample size increases if and only if the underlying
distribution is in essence a Pareto. In conjunction with a chi-square test of fit, it provides an asymptotically distribution-free
test of fit to the family of distributions with regularly varying tails at infinity. When the limit distribution holds, rank-size
plots obey Zipf’s law. The test can be used to detect departures from this Zipf–Pareto law.
相似文献
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The existence theorem of Minkowski for a polytope with given facet normals and areas is adapted to a data-analytic context.
More precisely, we show that a centered, random point sample arising from an absolutely continuous distribution in R
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can be uniquely mapped into such a polytope almost surely. With increasing sample size, the sequence of (scaled) polytopes
converges almost surely to a limiting convex body that is associated with the underlying distribution. An accompanying central
limit theorem is proved using methods from the theory of empirical processes.
Received January 28, 1999, and in revised form April 12, 1999. 相似文献
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We study a model of species survival recently proposed by Michael and Volkov. We interpret it as a variant of empirical processes, in which the sample size is random and when decreasing, samples of smallest numerical values are removed. Micheal and Volkov proved that the empirical distributions converge to the sample distribution conditioned not to be below a certain threshold. We prove a functional central limit theorem for the fluctuations. There exists a threshold above which the limit process is Gaussian with variance bounded below by a positive constant, while at the threshold it is half-Gaussian. 相似文献
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The central result is a limit theorem for not necessarily stationary processes resembling AR (p). Assumption of a vector limit distribution for standardized sample autocorrelations leads to the convergence of a vector limit distribution for ordinary sample partial autocorrelations, and to a clear relationship between the two limit distributions. The motivation is the study of the case p=1 by Mills and Seneta (1989, Stochastic Process Appl., 33, 151–161). The central result is used to explain the nature of the relationship between the two results of Quenouille in the classical stationary AR (p) setting. 相似文献
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In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions. 相似文献
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Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1987,39(1):457-472
Summary This paper is concerned with an extension of the problem of testing symmetry about zero of a distribution function. In order
to obtain the asymptotic null distribution of test statistics for the problem, a limit theorem is proved, which indeed plays
an essential role in the asymptotic theory of testing, problem for symmetry.
The Institute of Statistical Mathematics 相似文献
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Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献