**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Publication# Dispersion operators and resistant second-order functional data analysis

Abstract

Inferences related to the second-order properties of functional data, as expressed by covariance structure, can become unreliable when the data are non-Gaussian or contain unusual observations. In the functional setting, it is often difficult to identify atypical observations, as their distinguishing characteristics can be manifold but subtle. In this paper, we introduce the notion of a dispersion operator, investigate its use in probing the second-order structure of functional data, and develop a test for comparing the second-order characteristics of two functional samples that is resistant to atypical observations and departures from normality. The proposed test is a regularized M-test based on a spectrally truncated version of the Hilbert-Schmidt norm of a score operator defined via the dispersion operator. We derive the asymptotic distribution of the test statistic, investigate the behaviour of the test in a simulation study and illustrate the method on a structural biology dataset.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (34)

Related MOOCs (32)

Related publications (46)

Purely functional data structure

In computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure possesses the advantages of immutable objects: (full) persistency, quick copy of objects, and thread safety. Efficient purely functional data structures may require the use of lazy evaluation and memoization.

Functional programming

In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.

Second-order logic

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle).

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Learn about plasma applications from nuclear fusion powering the sun, to making integrated circuits, to generating electricity.

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Victor Panaretos, Soham Sarkar

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...

Thanh Trung Huynh, Quoc Viet Hung Nguyen, Thành Tâm Nguyên, Trung-Dung Hoang

Data redundancy has been one of the most important problems in data-intensive applications such as data mining and machine learning. Removing data redundancy brings many benefits in efficient data updating, effective data storage, and error-free query proc ...