{"title":"Estimation of trace-variogram using Legendre–Gauss quadrature","authors":"G. Sassi, Chang Chian","doi":"10.1214/22-bjps536","DOIUrl":null,"url":null,"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.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-bjps536","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
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.