Estimation of trace-variogram using Legendre–Gauss quadrature

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2022-09-01 DOI:10.1214/22-bjps536
G. Sassi, Chang Chian
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Abstract

. Functional Data Analysis is known for its application in several fields of science. In some cases, functional datasets are constituted by spatially indexed curves. The primary goal of this paper is to supply a straightforward and precise approach to interpolate these curves, i.e., the aim is to estimate a curve at an unmonitored location. It is proven that the best linear unbiased estimator for this unsampled curve is the solution of a linear system, where the coefficients and the constant terms of the system are formed using a function called trace-variogram. In this paper, we propose using Legendre-Gauss quadrature to estimate the trace-variogram. This estimator’s suitable numerical properties are shown in simulation studies for normal and non-normal datasets. Simulation results indicated that the proposed methodology outperforms the established estimation procedure. An R package was built and is available at the CRAN repository. The novel estimation methodology is illustrated with a real dataset on temperature curves from 35 weather stations in Canada.
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利用勒让德-高斯正交估计迹变差函数
。功能数据分析以其在几个科学领域的应用而闻名。在某些情况下,功能数据集由空间索引曲线组成。本文的主要目标是提供一种直接而精确的方法来插值这些曲线,即,目的是在未监测的位置估计曲线。证明了该无采样曲线的最佳线性无偏估计是线性系统的解,其中系统的系数和常数项由一个称为迹变函数的函数构成。本文提出用勒让德-高斯正交法估计迹变函数。对正态和非正态数据集的仿真研究表明了该估计器的数值特性。仿真结果表明,该方法优于现有的估计方法。我们构建了一个R包,并在CRAN存储库中提供。用加拿大35个气象站的温度曲线的真实数据集说明了这种新的估计方法。
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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