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The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.
The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.
The goal of this thesis is to treat the temporal tail dependence and the cross-sectional tail dependence of heavy tailed functional time series. Functional time series are aimed at modelling spatio-temporal phenomena; for instance rain, temperature, pollution on a given geographical area, with temporally dependent observations. Heavy tails mean that the series can exhibit much higher spikes than with Gaussian distributions for instance. In such cases, second moments cannot be assumed to exist, violating the basic assumption in standard functional data analysis based on the sequence of autocovariance operators. As for random variables, regular variation provides the mathematical backbone for a coherent theory of extreme values. The main tools introduced in this thesis for a regularly varying functional time series are its tail process and its spectral process. These objects capture all the aspects of the probability distribution of extreme values jointly over time and space. The development of the tail and spectral process for heavy tailed functional time series is followed by three theoretical applications. The first application is a characterization of a variety of indices and objects describing the extremal behavior of the series: the extremal index, tail dependence coefficients, the extremogram and the point process of extremes. The second is the computation of an explicit expression of the tail and spectral processes for heavy tailed linear functional time series. The third and final application is the introduction and the study of a model for the spatio-temporal dependence for functional time series called maxima of moving maxima of continuous functions (CM3 processes), with the development of an estimation method.
This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017) held in A Coruña, Spain, from 15 to 17 June 2017. The series of IWFOS workshops was initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008. Since then, many of the major advances in functional statistics and related fields have been periodically presented and discussed at the IWFOS workshops.
An increasing number of statistical problems and methods involve infinite-dimensional aspects. This is due to the progress of technologies which allow us to store more and more information while modern instruments are able to collect data much more effectively due to their increasingly sophisticated design. This evolution directly concerns statisticians, who have to propose new methodologies while taking into account such high-dimensional data (e.g. continuous processes, functional data, etc.). The numerous applications (micro-arrays, paleo- ecological data, radar waveforms, spectrometric curves, speech recognition, continuous time series, 3-D images, etc.) in various fields (biology, econometrics, environmetrics, the food industry, medical sciences, paper industry, etc.) make researching this statistical topic very worthwhile. This book gathers important contributions on the functional and operatorial statistics fields.
The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.Key features:• algorithic approaches • wavelets and nonlinear smoothers • graphical methods and data mining • biostatistics and bioinformatics • bagging and boosting • support vector machines • resampling methods
This volume, which highlights recent advances in statistical methodology and applications, is divided into two main parts. The first part presents theoretical results on estimation techniques in functional statistics, while the second examines three key areas of application: estimation problems in queuing theory, an application in signal processing, and the copula approach to epidemiologic modelling. The book’s peer-reviewed contributions are based on papers originally presented at the Marrakesh International Conference on Probability and Statistics held in December 2013.
New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.
This book offers a predominantly theoretical coverage of statistical prediction, with some potential applications discussed, when data and/ or parameters belong to a large or infinite dimensional space. It develops the theory of statistical prediction, non-parametric estimation by adaptive projection – with applications to tests of fit and prediction, and theory of linear processes in function spaces with applications to prediction of continuous time processes. This work is in the Wiley-Dunod Series co-published between Dunod (www.dunod.com) and John Wiley and Sons, Ltd.
Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.