Trimmed means for functional data

Fraiman, Ricardo; Muñiz, Graciela Inés Bolzón de

doi:10.1007/bf02595706

Cited by 284 publications

(268 citation statements)

References 12 publications

Supporting

Mentioning

263

Contrasting

Unclassified

Order By: Relevance

“…We first consider four models (M1-M4) with what we call ''magnitude'' contamination. These models were analyzed by Fraiman and Muniz (2001) and López-Pintado and Romo (2009). They all consist in adding some outliers to an elementary model M0 defined as…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Most of these multivariate depths are not adequate for high-dimensional data, therefore their applicability is restricted to low-dimensional vector observations. Recently, alternative notions of depth for functional data have been introduced which can be adapted to high-dimensional data without a large computational burden (see Fraiman and Muniz, 2001;Cuevas et al, 2006Cuevas et al, , 2007Cuesta-Albertos and Nieto-Reyes, 2008;Jörnsten, 2007 andRomo, 2009). In this paper we propose an alternative graph-based notion of depth which is simple, computationally fast, and can be easily adapted to high-dimensional data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A half-region depth for functional data

López‐Pintado

Romo

2011

Computational Statistics & Data Analysis

100

View full text Add to dashboard Cite

a b s t r a c tA new definition of depth for functional observations is introduced based on the notion of ''half-region'' determined by a curve. The half-region depth provides a simple and natural criterion to measure the centrality of a function within a sample of curves. It has computational advantages relative to other concepts of depth previously proposed in the literature which makes it applicable to the analysis of high-dimensional data. Based on this depth a sample of curves can be ordered from the center-outward and order statistics can be defined. The properties of the half-region depth, such as consistency and uniform convergence, are established. A simulation study shows the robustness of this new definition of depth when the curves are contaminated. Finally, real data examples are analyzed.

show abstract

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A half-region depth for functional data

López‐Pintado

Romo

2011

Computational Statistics & Data Analysis

100

View full text Add to dashboard Cite

show abstract

“…To compare their behavior, we have simulated curves from several models with some type of contamination. There are different ways of contaminating a continuous process; among others, we will use the ones in [2]. In all cases analyzed below we have considered two models and simulated seventy curves from each one.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Recently, the notion of depth has been extended to functional data. Fraiman and Muniz ( [2]) have proposed a depth for functions defined as the integral of univariate depths. Alternatively, López-Pintado and Romo ( [17]) have introduced a functional depth based on the proportion of bands including the curve graph.…”

Section: Introductionmentioning

confidence: 99%

Depth-based classification for functional data

López‐Pintado¹,

Romo²

2006

DIMACS Series in Discrete Mathematics And Theoretical Computer Science

View full text Add to dashboard Cite

Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods. Madrid, e-mail: juan.romo@uc3m.es. DIMACS Series in Discrete Mathematics and Theoretical Computer ScienceDepth-based classification for functional data Sara López-Pintado and Juan RomoAbstract. Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods.

show abstract

“…The idea of statistical depth has been recently extended to functional observations. Fraiman and Muniz (2001) proposed a definition of depth as the integral of univariate depths. López-Pintado and Romo (2006) have introduced and studied the band depth, which is a notion of functional depth based on the curves graphs.…”

Section: Introductionmentioning

confidence: 99%

Depth-based inference for functional data

López‐Pintado

Romo

2007

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

We propose robust inference tools for functional data based on the notion of depth for curves. We extend the ideas of trimmed regions, contours and central regions to functions and study their structural properties and asymptotic behavior. Next, we introduce a scale curve to describe dispersion in a sample of functions. The computational burden of these techniques is not heavy and so they are also adequate to analyze high-dimensional data. All these inferential methods are applied to different real data sets. AbstractWe propose robust inference tools for functional data based on the notion of depth for curves. We extend the ideas of trimmed regions, contours and central regions to functions and study their structural properties and asymptotic behavior. Next, we introduce a scale curve to describe dispersion in a sample of functions. The computational burden of these techniques is not heavy and so they are also adequate to analyze high-dimensional data. All these inferential methods are applied to different real data sets.

show abstract

Trimmed means for functional data

Cited by 284 publications

References 12 publications

A half-region depth for functional data

A half-region depth for functional data

Depth-based classification for functional data

Depth-based inference for functional data

Contact Info

Product

Resources

About