Dates: 26-28 August 2016 (Friday afternoon to Sunday afternoon)
Venue: Auditorium/Congress Palace Principe Felipe, Spain.
Organizers: Ana Colubi and Gil Gonzalez-Rodriguez.

Hans-Georg Mueller, University of California Davis, USA.
Hannu Oja, University of Turku, Finland. Cancelled, new talk by
Frederic Ferraty, Mathematics Institute of Toulouse, France.
Jane-Ling Wang, University of California Davis, USA.

The new interactive programme provides a quick overview of the schedule of the summer course, with easy access to all the sessions including their location as well as all abstracts.

You can add it to the bookmarks of your favourite device in order to access all the information during the conference.

Alternatively you can check the static list of abstracts (optimized for Mozilla and Google Chrome) as well as the list of participants.

CRoNoS FDA 2016 Programme Changes

Hans-Georg Mueller and Jane-Ling Wang, University of California, Davis, USA.

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points for many units or subjects. These are instances of "functional data". Functional Data Analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions, or can thought of as being generated by latent functions.

We provide an introduction into the most commonly used methods of FDA. These include Functional Principal Component Analysis (FPCA) and the related concept of modes of variation, which is based on simple statistical notions such as mean and covariance function of a random process that can be inferred from the data. FPCA is an important dimension reduction tool and in sparse data situations can be used to impute functional data that are sparsely observed.

Another core topic of FDA is functional regression, where one pairs functions or scalars as predictors with responses that are also functions or scalars. A classical model is functional linear regression, which can be implemented for combinations of vectors and functions in both predictors and responses. For the case where the predictors include functions, a difficult step that requires regularization is the inversion of a covariance operator, which is an ill-posed problem. Such an inverse problem is also related to some forms of functional correlation, which will be another core topic.

Beyond the linear modeling approaches, nonlinear methods have found increasing interest. These include polynomial and quadratic regression relations, dimension reduction methods such as additive, continuously additive and index models, and other nonlinear approaches. Such approaches are also useful for shape constrained functional data such as samples of densities.

Further topics of interest that may be covered are warping and manifold learning, the learning of time dynamics from observed realizations of the underlying stochastic process, multivariate and repeatedly observed functional data and stringing of high-dimensional data into functional data.

Slides of presentations

Hannu Oja, University of Turku, Finland. Cancelled, new talk

Slides of presentation

Gil Gonzalez-Rodriguez, University of Oviedo, Spain.

Hilbert spaces are frequently used in statistics as a framework to deal with general random elements, specially with functional-valued random variables. The scarcity of common parametric distribution models in this context makes it important to develop non-parametric techniques,and among them, bootstrap has already proved to be specially valuable.

The aim is to illustrate how to derive consistent bootstrap approaches in separable Hilbert spaces. Naive bootstrap, bootstrap with arbitrary sample size, wild bootstrap, and several weighted bootstrap methods, including, e.g., double bootstrap, and bootstrap generated by deterministic weights, with the particular case of delete$-h$ jackknife,will be obtained as examples within the considered framework. The main results concern the bootstrapped sample mean, however since many frequent statistics can be written in terms of means by considering suitable spaces, the applicability is notable. An illustration to show how to employ the approach in the context of a functional regression problem is discussed.

Slides of presentation

Registration includes attendance to the Satellite CRoNoS Workshop on Functional Data Analysis

Workshop and Summer Course Dinner (Saturday 27th August 2016)

35€

PhD students and Early Career Investigators (who have obtained their PhD degree in 2009 or after) can apply for a limited number of grants of 500 Euro for accommodation and traveling and will have their fees for the course waived.

• In order to apply for the grants candidates should submit their CV by e-mail to cronos.cost@gmail.com.
• Deadline for applications: 15th March 2015.
• Granted candidates will be informed by e-mail within 1 week after the deadline and must send their flight tickets and accommodation booking 15 days after the application deadlines (30th of March) to cronos.cost@gmail.com to secure their grants. Otherwise, their grants will be revoked and assigned to other candidate.
• The granted candidates must attend all the sessions of the course and sign the attendance list in order to obtain their grants.