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Nonparametric inference for functional data: auto-covariance function, classification and clustering

Grant number: 14/26414-9
Support type:Scholarships abroad - Research
Effective date (Start): August 15, 2015
Effective date (End): July 15, 2016
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Statistics
Principal researcher:Ronaldo Dias
Grantee:Ronaldo Dias
Host: Daniela Witten
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: University of Washington, United States  
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID


In recent years, with the advent of new technologies, functional dada has beenobserved and collected more often in different areas of science and technology. Although data are gathered as finite vector and it may contain measurement errors, its functional nature has to be taken into account. Furthermore, in Functional Data Analysis (FDA) there are situations where one needs to access information from different sources or different groups/classes/categories of curves . In other words, classificationand clustering is necessary, as it is in several areas of science and technology. However, in FDA the functional nature of data must be kept. For theoretical and practical reason the estimation of covariancefunction have been calling the attention of practitioners, engineers,scientists and many other professionals. In addition, it is well known that inStatistical Learning problems, particularly inclassification, there is the need of a kernel function satisfying Merce'sconditons( see \cite{wahb:1990} ). It is straightforward to show that covariance function, under Gaussian Process assumption, satisfies completely these conditions. Consequently, the development of good, in some sense, automatic procedure, solely using information from data, toestimate the covariance function is necessary.There many applications where the estimation of spatial and spatial-temporal covariance function is needed. See for example problems in Image Classification. In supervised learning and many classification procedures, the notion of similarity between data points is crucial. The basic similarity assumption that points with inputs $\XX$ which are close are likely to have similar target values $\Y$. Hence, training points that are near to a test point shouldbe informative about the prediction at that point. Under the Gaussian processviewpoint it is the covariance function that defines nearness or similarity. Moreover, the study of techniques for spatial functional data has recently attracted the interest of the functional data analysis researchers due to the fact that many real applicationsdeal with data that are observed in the space that changes continuously in time. It is the case when samples of functions are observed in different sites of a region. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LENZI, AMANDA; DE SOUZA, CAMILA P. E.; DIAS, RONALDO; GARCIA, NANCY L.; HECKMAN, NANCY E. Analysis of aggregated functional data from mixed populations with application to energy consumption. ENVIRONMETRICS, v. 28, n. 2 MAR 2017. Web of Science Citations: 2.

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