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Suppose {Xnn?-0} are random variables such that for normalizing constants an>0, bn, n?0 we have Yn(·)=(X[n, ·]-bn/an ? Y(·) in D(0.∞) . Then an and bn must in specific ways and the process Y possesses a scaling property. If {Nn} are positive integer valued random variables we discuss when YNn → Y and Y'n=(X[Nn]-bn)/an ? Y'. Results given subsume random index limit theorems for convergence to Brownian motion, stable processes and extremal processes. 相似文献
64.
Bivariate stable distributions are defined as those having a domain of attraction, where vectors are used for normalization. These distributions are identified and their domains of attraction are given in a number of equivalent forms. In one case, marginal convergence implies joint convergence. A bivariate optional stopping property is given. Applications to bivariate random walk are suggested. 相似文献
65.
Let Xt = Σ∞j=-∞ cjZt - j be a moving average process where {Zt} is iid with common distribution in the domain of attraction of a stable law with index , 0 < < 2. If 0 < < 2, E|Z1| < ∞ and the distribution of |Z1|and |Z1Z2| are tail equivalent then the sample correlation function of {X1} suitably normalized converges in distribution to the ratio of two dependent stable random variables with indices and /2. This is in sharp contrast to the case E|Z1| = ∞ where the limit distribution is that of the ratio of two independent stable variables. Proofs rely heavily on point process techniques. We also consider the case when the sample correlations are asymptotically normal and extend slightly the classical result. 相似文献
66.
Sidney I. Resnick 《Stochastic Processes and their Applications》1973,1(1):67-82
{Xn,n?1} are i.i.d. random variables with continuous d.f. F(x). Xj is a record value of this sequence if Xj>max{X1,…,Xj?1}. Consider the sequence of such record values {XLn,n?1}. Set R(x)=-log(1?F(x)). There exist Bn > 0 such that . in probability (i.p.) iff i.p. iff → ∞ as x→∞ for all k>1. Similar criteria hold for the existence of constants An such that XLn?An → 0 i.p. Limiting record value distributions are of the form N(-log(-logG(x))) where G(·) is an extreme value distribution and N(·) is the standard normal distribution. Domain of attraction criteria for each of the three types of limit laws can be derived by appealing to a duality theorem relating the limiting record value distributions to the extreme value distributions. Repeated use is made of the following lemma: If , then XLn=Y0+…+Yn where the Yj's are i.i.d. and . 相似文献
67.
A photoreactivationless mutant of Saccharomyces cerevisiae 总被引:10,自引:0,他引:10
M A Resnick 《Photochemistry and photobiology》1969,9(4):307-312
Abstract— A mutant of S. cerevisiue has been isolated that is incapable of photoreactivating u.v.-induced lethal damage. The mutant resulted from mutation of the chromosomal gene PHR 1, which was determined to be dominant. This gene is involved with the production of photoreactivating enzyme. 相似文献
68.
A heavy tailed time series that can be represented as an infinite moving average has the property that the sample autocorrelation function (ACF) at lag h converges in probability to a constant (h), although the mathematical correlation typically does not exist. For many nonlinear heavy tailed models, however, the sample ACF at lag h converges in distribution to a nondegenerate random variable. In this paper, a test for (non)linearity of a given infinite variance time series is constructed, based on subsample stability of the sample ACF. The test is applied to several real and simulated datasets. 相似文献
69.
We consider the analysis of time series data which require models with a heavy-tailed marginal distribution. A natural model to attempt to fit to time series data is an autoregression of order p, where p itself is often determined from the data. Several methods of parameter estimation for heavy tailed autoregressions have been considered, including Yule–Walker estimation, linear programming estimators, and periodogram based estimators. We investigate the statistical pitfalls of the first two methods when the models are mis-specified—either completely or due to the presence of outliers. We illustrate the results of our considerations on both simulated and real data sets. A warning is sounded against the assumption that autoregressions will be an applicable class of models for fitting heavy tailed data. 相似文献
70.