Search results for "Functional data"
showing 10 items of 46 documents
Common functional component modelling
2005
Functional data analysis (FDA) has become a popular technique in applied statistics. In particular, this methodology has received considerable attention in recent studies in empirical finance. In this talk we discuss selected topics of functional principal components analysis that are motivated by financial data.
Functional linear models for the analysis of similarity of waveforms
2018
In seismology methods based on waveform similarity analysis are adopted to identify sequences of events characterized by similar fault mechanism and prop- agation pattern. Seismic waves can be considered as spatially interdependent three dimensional curves depending on time and the waveform similarity analysis can be configured as a functional clustering approach, on the basis of which the member- ship is assessed by the shape of the temporal patterns. For providing qualitative ex- traction of the most important information from the recorded signals we propose an integration of the metadata, related to the waves, as explicative variables of a func- tional linear models. The temporal pattern…
Changes in power curve shapes as an indicator of fatigue during dynamic contractions.
2010
The purpose of this study was to analyze exercise-induced leg fatigue during a dynamic fatiguing task by examining the shapes of power vs. time curves through the combined use of several statistical methods: B-spline smoothing, functional principal components and (supervised and unsupervised) classification. In addition, granulometric size distributions were also computed to allow for comparison of curves coming from different subjects. Twelve physically active men participated in one acute heavy-resistance exercise protocol which consisted of five sets of 10 repetition maximum leg press with 120 s of rest between sets. To obtain a smooth and accurate representation of the data, a basis of …
A new approach for clustering of effects in quantile regression
2017
In this paper we aim at nding similarities among the coefficients from a multivariate regression. Using a quantile regression coefficients modeling, the effect of each covariate, given a response (also multivariate) is a curve in the multidimensional space of the percentiles. Collecting all the curves, describing the effects of each covariate on each response variable, we could be able to assess if only one or more covariates have same effects on different responses.
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
2013
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of …
Detecting clusters in spatially correlated waveforms
2017
Seismic networks often record signals characterized by similar shapes that provide important information according to their geographic positions. We propose an approach to identify homogeneous clusters of seismic waves, combining analysis of waveforms with metadata and spectrogram information. In waveforms clustering, cross-correlation measures between signals may presents some limitations, so we refer to more recent contributes relating data-depth based clustering analysis. The mechanism for alignment is also an important topic of the analysis: warping (or aligning) procedures identify nuisance effects in phase variation, that, if ignored, may result in a possible loss of information and t…
Stochastic algorithms for robust statistics in high dimension
2016
This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the me…
Conditional Bias Robust Estimation of the Total of Curve Data by Sampling in a Finite Population: An Illustration on Electricity Load Curves
2020
Abstract For marketing or power grid management purposes, many studies based on the analysis of total electricity consumption curves of groups of customers are now carried out by electricity companies. Aggregated totals or mean load curves are estimated using individual curves measured at fine time grid and collected according to some sampling design. Due to the skewness of the distribution of electricity consumptions, these samples often contain outlying curves which may have an important impact on the usual estimation procedures. We introduce several robust estimators of the total consumption curve which are not sensitive to such outlying curves. These estimators are based on the conditio…
Functional Data Analysis for ECG Recordings of Paroxysmal Atrial Fibrillation Patients Before and After Pulmonary Vein Isolation
2018
Pulmonary vein isolation is the cornestone of current ablation techniques for patients with paroxysmal atrial fibrillation in order avoid recurrences of the arrhythmia and maintain sinus rhythm. This study aimed to analyse the existence of significant variations in surface ECG after pulmonary vein isolation by means of functional data analysis. 12 consecutive unselected patients suffering from paroxysmal atrial fibrillation who underwent catheter ablation were included in the study. Each patient was monitored in sinus rhythm before and after catheter ablation. P-waves of bipolar lead II were delineated. Functional data were fitted from these segments and the first and second derivatives eva…
Assessing the Beneficial Effects of Economic Growth: The Harmonic Growth Index
2011
In this paper we introduce the multidimensional notion of harmonic growth as a situation of diffused well-being associated to an increase of per capita GDP. We say that a country experienced a harmonic growth if during the observed period all the key indicators, proxies of the endogenous and exogenous forces driving population well-being, show a significantly common pattern with the income dynamics. The notion is operationalized via an index of time series harmony which follows the functional data analysis approach. This Harmonic Growth Index (HGI) is based on comparisons between the coefficients from cubic B-splines interpolation. Such indices are then synthesized in order to provide the g…