Imm-s) ^ I Limit Laws for Extreme Order Statistics from Strong-mixing Processes"''
نویسنده
چکیده
This paper considers the possible limit laws for a sequence of normalized extreme order statistics (maximum, second maximum, etc.) from a stationary strong-mixing sequence of random variables. It extends the work of Loynes who treated only the maximum process. The maximum process leads to limit laws that are the same three types that occur when the underlying process is a sequence of independent random variables. The results presented here show that the possible limit laws for the k-th maximum process (k>l) from a strongmixing sequence form a larger class than can occur in the independent case.
منابع مشابه
Free point processes and free extreme values
We continue here the study of free extreme values begun in [3]. We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure ([15], [2]). We relate this convergence to the free extremal laws introduced in [3] and give the limit laws for free order statistics.
متن کاملStrong Gaussian Approximations of Product-limit and Quantile Processes for Strong Mixing and Censored Data
In this paper, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rat...
متن کاملHitting Time Statistics and Extreme Value Theory
We consider discrete time dynamical system and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa. We apply these resu...
متن کاملOuter and Inner Confidence Intervals Based on Extreme Order Statistics in a Proportional Hazard Model
Let Mi and Mi be the maximum and minimum of the ith sample from k independent sample with different sample sizes, respectively. Suppose that the survival distribution function of the ith sample is F ̄i = F ̄αi, where αi is known and positive constant. It is shown that how various exact non-parametric inferential proce- ′ dures can be developed on the basis of Mi’s and Mi ’s for distribution ...
متن کاملAsymptotic Expansions for Stochastic Processes
The central limit theorems are the basis of the large sample statistics. In estimation theory, the asymptotic efficiency is evaluated by the asymptotic variance of estimators, and in testing statistical hypotheses, the critical region of a test is determined by the normal approximation. Though asymptotic properties of statistics are based on central limit theorems, the accuracy of their approxi...
متن کامل