WAVELET ESTIMATION OF THE COVARIANCE OF ALMOST PERIODICALLY CORRELATED PROCESSES AND STUDY OF ASYMPTOTIC PROPERTIES IN A CONTEXT OF WEAK DEPENDENCE

Moussa Koné, V. Monsan
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Abstract

We construct a multiresolution estimator and study its asymptotic properties. The estimation of the coefficients of the covariance decomposition of an almost periodically correlated process on a wavelet basis is dealt with. It is found that the covariance relates to random variables satisfying a weak dependence structure of quasi-association type. In this context, we first recall a method for constructing a wavelet base, with the decomposition of the covariance function in this base and obtain a set of coefficients to be estimated. We then construct an estimator of the coefficients obtained, under specific sampling conditions (jitter or delay). Following are the three main results obtained in the paper: • The first result concerns the almost sure convergence of the multiresolution estimator built from the model of the spectral covariance estimator. • The second result establishes consistency under the quasi-association hypothesis, a convergence rate is provided. • The third result establishes the asymptotic normality of the estimator.
弱相关条件下概周期相关过程协方差的小波估计及渐近性质的研究
构造了一个多分辨率估计量,并研究了它的渐近性质。研究了一种基于小波变换的近周期相关过程的协方差分解系数估计问题。发现协方差与满足准关联型弱依赖结构的随机变量有关。在这种情况下,我们首先回顾了一种构造小波基的方法,并对该基中的协方差函数进行分解,得到一组待估计的系数。然后,在特定的采样条件下(抖动或延迟),我们构造得到的系数的估计量。以下是本文获得的三个主要结果:•第一个结果涉及从谱协方差估计器模型构建的多分辨率估计器的几乎肯定收敛性。•第二个结果在拟关联假设下建立了一致性,给出了一个收敛速率。•第三个结果建立了估计量的渐近正态性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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