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Selection from a finite population is used in several procedures in statistics, among others in bootstrap and permutation methods. In this paper we give a survey of some recent results for selection in “nonstandard” situations, i.e. in cases when the negligibility condition of classical central limit theory is not satisfied. These results enable us to describe the asymptotic properties of bootstrap...
Max-stable processes arise as limits in distribution of component-wise maxima of independent processes, under suitable centering and normalization. Therefore, the class of max-stable processes plays a central role in the study and modeling of extreme value phenomena. This chapter starts with a review of classical and some recent results on the representations of max-stable processes. Recent results...
The purpose of this note is to prove a lower bound for the estimation of the memory parameter of a stationary long memory process. The memory parameter is defined here as the index of regular variation of the spectral density at 0. The rates of convergence obtained in the literature assume second order regular variation of the spectral density at zero. In this note, we do not make this assumption,...
We present here an extension of the theorem on asymptotic behavior of Fejér graph integrals stated in [7] to the case of integrals with more general kernels which allow for tapering. As a corollary, asymptotic normality results for tapered estimators are derived.
From a theoretical perspective, scale invariance, or simply scaling, can fruitfully be modeled with classes of multifractal stochastic processes, designed from positive multiplicative martingales (or cascades). From a practical perspective, scaling in real-world data is often analyzed by means of multiresolution quantities. The present contribution focuses on three different types of such multiresolution...
We investigate the properties of multifractal products of the exponential of Ornstein-Uhlenbeck processes driven by Lévy motion. The conditions on the mean, variance and covariance functions of these processes are interpreted in terms of the moment generating functions. We provide two examples of tempered stable and normal tempered stable distributions. We establish the corresponding log-tempered...
This paper revisits the concept of dependence.We view statistical dependence as the state of variables being influenced by others. Our viewpoint accords well with the daily understanding of the notion of dependence, while classical dependence measures such as Pearson’s correlation coefficient, Kendall’s τ and Spearman’s ρ have different meanings.With this understanding of dependence, we introduce...
This paper deals with the so-called S-estimation, which is known to have up to 50% breakdown point and therefore yielding one of the most robust estimators against outlier values, in a multiple linear regression when the errors are dependent. We mainly focus on the case when these errors exhibit a long range dependence pattern.We establish asymptotic normality of the slope estimator via some maximal...
Horváth et al. [8] developed a monitoring procedure for detecting a change in the parameters of a linear regression model having independent and identically distributed errors. We extend these results to allow for dependent errors, which need not be independent of the stochastic regressors, and we also provide a class of consistent variance estimators. Our results cover strongly mixing errors as an...
The danger of confusing long-range dependence with non-stationarity has been pointed out by many authors. Finding an answer to this difficult question is of importance to model time-series showing trend-like behavior, such as river runoff in hydrology, historical temperatures in the study of climates changes, or packet counts in network traffic engineering. The main goal of this paper is to...
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