Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments

Pub Date : 2020-01-01 DOI:10.1051/PS/2020021
J. Azaïs, F. Bachoc, A. Lagnoux, Thi Mong Ngoc Nguyen
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引用次数: 2

Abstract

We consider the semi-parametric estimation of the scale parameter of the variogram of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based both on quadratic variations and the moment method. We provide asymptotic approximations of the mean and variance of this estimator, together with asymptotic normality results, for a large class of Gaussian processes. We allow for general mean functions, provide minimax upper bounds and study the aggregation of several estimators based on various variation sequences. In extensive simulation studies, we show that the asymptotic results accurately depict the finite-sample situations already for small to moderate sample sizes. We also compare various variation sequences and highlight the efficiency of the aggregation procedure.
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具有平稳增量的高斯过程变差尺度参数的半参数估计
考虑了已知光滑度的一维高斯过程变差函数尺度参数的半参数估计。我们提出了一种基于二次变分和矩量法的估计方法。我们给出了这一估计量的均值和方差的渐近逼近,并给出了一大类高斯过程的渐近正态性结果。我们考虑了一般的均值函数,提供了极大极小上界,并研究了基于各种变异序列的几个估计量的集合。在广泛的模拟研究中,我们表明渐近结果已经准确地描述了小到中等样本量的有限样本情况。我们还比较了各种变异序列,并强调了聚合过程的效率。
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