On the use of the bootstrap for estimating functions with functional data

Cuevas, Antonio; Febrero, Manuel; Fraiman, Ricardo

doi:10.1016/j.csda.2005.10.012

Cited by 154 publications

(129 citation statements)

References 17 publications

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“…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%

A half-region depth for functional data

López‐Pintado

Romo

2011

Computational Statistics & Data Analysis

100

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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.

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Section: Introductionmentioning

confidence: 99%

A half-region depth for functional data

López‐Pintado

Romo

2011

Computational Statistics & Data Analysis

100

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“…Not only it is important to obtain a consistent estimator, we are also interested in estimating the variability associated with the descriptive statistics and constructing its confidence intervals (CIs). When such a problem arises, re-sampling methodology especially bootstrapping turns out to be the only practical alternative (Cuevas et al, 2006;McMurry and Politis, 2011). Pioneering work by Mahalanobis (1946), Hartigan (1969), Efron (1979), Hall (1992), Simon (1993) and Efron and Tibshirani (1993) show the use of bootstrap techniques to compute valid statistical measures, such as CIs, by means of computational-intensive simulations using only the observed data.…”

Section: Introductionmentioning

confidence: 99%

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Shang

2014

Communications in Statistics - Simulation and Computation

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Re-sampling methods for estimating the distribution of descriptive statistics of functional data are considered. Through Monte-Carlo simulations, we compare the performance of several re-sampling methods commonly used for estimating the distribution of descriptive statistics.We introduce two re-sampling methods that rely on functional principal component analysis, where the scores were randomly drawn from multivariate normal distribution and Stiefel manifold. Illustrated by one-dimensional Canadian weather station data and two-dimensional bone shape data, the re-sampling methods provide a way of visualizing the distribution of descriptive statistics for functional data.

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“…It is important to display the estimated mean functions by taking into account these limits. We have estimated these mean functions using a bootstrap method proposed in [4]. First, if we do not consider the different pump flows we can estimate some kind of global mean function.…”

Section: Local Functional Anovamentioning

confidence: 99%

Statistical tools and control of internal lubricant content of inhalation grade HPMC capsules during manufacture

Ayala

Dı́ez²,

Gassó

et al. 2016

International Journal of Pharmaceutics

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Elsevier Ayala, G.; Diez, F.; Gasso Matoses, MT.; Jones, BE.; Martin-Portugues, R.; MartinPortugues, R.; Ramiro-Aparicio, J. (2016) AbstractPulmonary delivery is being becoming a popular route for delivering active pharmaceutical ingredients that cannot be administered through by the standard oral route, as well as offering an improved alternative to the parenteral route. The use of hard capsules in dry powder inhalers (DPIs) to deliver formulations to the lung has been in use since 1970, and recently there has been an interest in changing from metered-dose devices to capsulebased ones because they are simple to formulate, cheap to manufacture, and patient-friendly. The original inhalation grade hard capsules were made from gelatin, which becomes brittle when exposed to low humidities. Inhalation grade hypromellose (HPMC, carrageenan gelling agent) has been developed in the last few years to overcome come this problem and has been shown to have better aerosolization properties. Hard capsules are made by a dipping process in which a surface lubricant is an essential processing aid for removing dried capsule shells from the manufacturing pins. This lubricant has been shown to have an effect on powder retention in capsules that are used for the inhalation of medicines. The capsule manufacturing process depends on many factors. The response is a function giving the the internal lubricant content (ILC) from 0 to 48 hours. Two of them were chosen by experts in order to evaluate their influ- Additionally we want to know if the mean ILC is between the tolerance limits. A bootstrap confidence region is used to estimate local confidence regions of the response.

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On the use of the bootstrap for estimating functions with functional data

Cited by 154 publications

References 17 publications

A half-region depth for functional data

A half-region depth for functional data

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Statistical tools and control of internal lubricant content of inhalation grade HPMC capsules during manufacture

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