Search results for "functional data"
showing 10 items of 46 documents
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 …
Functional Principal Component Analysis for the explorative analysis of multisite-multivariate air pollution time series with long gaps
2013
The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and…
Clusters of effects curves in quantile regression models
2018
In this paper, we propose a new method for finding similarity of effects based on quantile regression models. Clustering of effects curves (CEC) techniques are applied to quantile regression coefficients, which are one-to-one functions of the order of the quantile. We adopt the quantile regression coefficients modeling (QRCM) framework to describe the functional form of the coefficient functions by means of parametric models. The proposed method can be utilized to cluster the effect of covariates with a univariate response variable, or to cluster a multivariate outcome. We report simulation results, comparing our approach with the existing techniques. The idea of combining CEC with QRCM per…
Estimation of total electricity consumption curves by sampling in a finite population when some trajectories are partially unobserved
2019
International audience; Millions of smart meters that are able to collect individual load curves, that is, electricity consumption time series, of residential and business customers at fine scale time grids are now deployed by electricity companies all around the world. It may be complex and costly to transmit and exploit such a large quantity of information, therefore it can be relevant to use survey sampling techniques to estimate mean load curves of specific groups of customers. Data collection, like every mass process, may undergo technical problems at every point of the metering and collection chain resulting in missing values. We consider imputation approaches (linear interpolation, k…
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…
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.
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…
Local characteristics of functional marked point processes with applications to seismic data
2022
We present a family of local inhomogeneous mark-weighted summary statistics for general marked point processes. These capture various types of local dependence structures depending on the specified involved weight function. We use them to propose a local random labeling test. This procedure enables us to identify points and thus regions where the random labeling assumption does not hold, for example, when the (functional) marks are spatially dependent. We further present an application to a seismic point pattern with functional marks provided by seismic waveforms. Indeed, despite the relatively long history of point process theory, few approaches to analyzing spatial point patterns where th…
Functional principal component analysis of quantile curves
2017
Literature on functional data analysis is mainly focused on estimation of individuals curves and characterization of average dynamics. The idea underlying this proposal is to focus attention on other particular features of the distribution of the observed data, moving from mean functions towards functional quantiles. The motivating examples are functional data sets that are collections of high frequency data recorded along time. As quantiles provide information on various aspects of a time series, we propose a modelling framework for the joint estimation of functional quantiles, varying along time, and functional principal components, summarizing some common dynamics shared by the functiona…
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…