55 research outputs found

    A Depth for Censured Functional Data

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    Censured functional data are becoming more recurrent in applications. In those cases, the existing depth measure are useless. In this paper, an approach for measuring depths of censured functional data is presented. Its performance for finite samples is tested by simulation, showing that the new depth agrees with a integrated depth for uncensured functional data.Antonio ElĂ­as is supported by the Spanish Ministerio de EducaciĂłn, Cultura y Deporte under grant FPU15/00625. Antonio ElĂ­as and RaĂșl JimĂ©nez are partially supported by the Spanish Ministerio de EconomĂ­a y Competitividad under grant ECO2015-66593-P

    Functional Data Analysis of Amplitude and Phase Variation

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    The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude variability and is termed phase variation. The presence of phase variability artificially often inflates data variance, blurs underlying data structures, and distorts principal components. While the separation and/or removal of phase from amplitude data is desirable, this is a difficult problem. In particular, a commonly used alignment procedure, based on minimizing the L2\mathbb{L}^2 norm between functions, does not provide satisfactory results. In this paper we motivate the importance of dealing with the phase variability and summarize several current ideas for separating phase and amplitude components. These approaches differ in the following: (1) the definition and mathematical representation of phase variability, (2) the objective functions that are used in functional data alignment, and (3) the algorithmic tools for solving estimation/optimization problems. We use simple examples to illustrate various approaches and to provide useful contrast between them.Comment: Published at http://dx.doi.org/10.1214/15-STS524 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Statistics of time warpings and phase variations

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    Many methods exist for one dimensional curve registration, and how methods compare has not been made clear in the literature. This special section is a summary of a detailed comparison of a number of major methods, done during a recent workshop. The basis of the comparison was simultaneous analysis of a set of four real data sets, which engendered a high level of informative discussion. Most research groups in this area were represented, and many insights were gained, which are discussed here. The format of this special section is four papers introducing the data, each accompanied by a number of analyses by different groups, plus a discussion summary of the lessons learned

    Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics

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    We review recent advances in Object Oriented Spatial Statistics, a system of ideas, algorithms and methods that allows the analysis of high dimensional and complex data when their spatial dependence is an important issue. At the intersection of different disciplines – including mathematics, statistics, computer science and engineering – Object Oriented Spatial Statistics provides the right perspective to address key problems in varied contexts, from Earth and life sciences to urban planning. We illustrate a few paradigmatic methods applied to problems of prediction, classification and smoothing, giving emphasis to the key ideas Object Oriented Spatial Statistics relies upon

    On the role of statistics in the era of big data: A call for a debate

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    While discussing the plenary talk of Dunson (2016) at the 48th Scientific Meeting of the Italian Statistical Society, I formulated a few general questions on the role of statistics in the era of big data which stimulated an interesting debate. They are reported here with the aim of engaging a larger audience on an issue which promises to change radically our discipline and, more generally, science as we know it. But is it so

    Functional Data Analysis of Amplitude and Phase Variation

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    The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude variability and is terme
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