arXiv subjects

Sara López-Pintado

Publications and source records attributed to Sara López-Pintado.

3 recordsLinked to original sources

arXiv2026

Depth-based estimation for multivariate functional data with phase variability

In the context of multivariate functional data with individual phase variation, we develop a robust depth-based approach to estimate the main pattern function when cross-component time warping is also present. In particular, we consider the latent deformation model (Carroll and Müller, 2023) in which the different components of a multivariate functional variable are also time-distorted versions of a common template function. Rather than focusing on a particular functional depth measure, we discuss the necessary conditions on a depth function to be able to provide a consistent estimation of the central pattern, considering different model assumptions. We evaluate the method performance and its robustness against atypical observations and violations of the model assumptions through simulations, and illustrate its use on two real data sets.

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arXiv2020

A notion of depth for sparse functional data

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It has also been used as a building block for functional outlier detection methods and classification. Several notions of depth for functional data were introduced in the literature in the last few decades. These functional depths can only be directly applied to samples of curves measured on a fine and common grid. In practice, this is not always the case, and curves are often observed at sparse and subject dependent grids. In these scenarios the usual approach consists in estimating the trajectories on a common dense grid, and using the estimates in the depth analysis. This approach ignores the uncertainty associated with the curves estimation step. Our goal is to extend the notion of depth so that it takes into account this uncertainty. Using both functional estimates and their associated confidence intervals, we propose a new method that allows the curve estimation uncertainty to be incorporated into the depth analysis. We describe the new approach using the modified band depth although any other functional depth could be used. The performance of the proposed methodology is illustrated using simulated curves in different settings where we control the degree of sparsity. Also a real data set consisting of female medflies egg-laying trajectories is considered. The results show the benefits of using uncertainty when computing depth for sparse functional data.

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arXiv2007

Functional analysis via extensions of the band depth

The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths of a set of multivariate observations translates to a center-outward ordering of the data. Thus, data depth provides a generalization of the median to a multivariate setting (the deepest observation), and can also be used to screen for extreme observations or outliers (the observations with low data depth). Data depth has been used in the development of a wide range of robust and non-parametric methods for multivariate data, such as non-parametric tests of location and scale [Li and Liu (2004)], multivariate rank-tests [Liu and Singh (1993)], non-parametric classification and clustering [Jornsten (2004)], and robust regression [Rousseeuw and Hubert (1999)]. Many different notions of data depth have been developed for multivariate data. In contrast, data depth measures for functional data have only recently been proposed [Fraiman and Muniz (1999), López-Pintado and Romo (2006a)]. While the definitions of both of these data depth measures are motivated by the functional aspect of the data, the measures themselves are in fact invariant with respect to permutations of the domain (i.e. the compact interval on which the functions are defined). Thus, these measures are equally applicable to multivariate data where there is no explicit ordering of the data dimensions. In this paper we explore some extensions of functional data depths, so as to take the ordering of the data dimensions into account.

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