Functional ANOVA starting from discrete data: an application to air quality data

Estévez-Pérez, Graciela; Vilar, José A.

doi:10.1007/s10651-012-0231-2

Cited by 19 publications

(11 citation statements)

References 30 publications

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“…To detect differences in the mean functions of two independent samples of curves Ramsay and Silverman (2005) introduced a pointwise t-test, Zhang et al (2010) presented an L 2 -norm-based test, Horváth et al (2013) proposed a test based on the sample means of the curves and Staicu et al (2014) developed a pseudolikelihood ratio test. Extension to k independent samples of curves was discussed in Cuevas et al (2004), Estévez-Pérez and Vilar (2008) and Laukaitis and Račkauskas (2005), who proposed analysis-of-variance like testing procedures for testing the equality of mean functions. For detecting differences in the covariance functions of independent samples of curves Ferraty et al (2007) proposed a factor-based test, Kraus and Panaretos (2012) introduced a regularized M-test and Fremdt et al (2012) proposed a χ 2test.…”

Section: Existing Approaches For Two-sample Testingmentioning

confidence: 99%

“…Extension to k independent samples of curves was discussed in Cuevas et al . (), Estévez‐Pérez and Vilar () and Laukaitis and Racˇkauskas (), who proposed analysis‐of‐variance like testing procedures for testing the equality of mean functions. For detecting differences in the covariance functions of independent samples of curves Ferraty et al .…”

Section: Introductionmentioning

confidence: 99%

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A Two-Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis

Pomann

Staicu

Ghosh

2016

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary Motivated by an imaging study, this paper develops a nonparametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to formally compare white matter tract profiles between healthy individuals and multiple sclerosis patients, as assessed by conventional diffusion tensor imaging measures. We propose to decompose the curves using functional principal component analysis of a mixture process, which we refer to as marginal functional principal component analysis. This approach reduces the dimension of the testing problem in a way that enables the use of traditional nonparametric univariate testing procedures. The procedure is computationally efficient and accommodates different sampling designs. Numerical studies are presented to validate the size and power properties of the test in many realistic scenarios. In these cases, the proposed test has been found to be more powerful than its primary competitor. Application to the diffusion tensor imaging data reveals that all the tracts studied are associated with multiple sclerosis and the choice of the diffusion tensor image measurement is important when assessing axonal disruption.

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Section: Existing Approaches For Two-sample Testingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Two-Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis

Pomann

Staicu

Ghosh

2016

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Estévez-Pérez & Vilar (2008) extended the method to k-sample cases and applied it to air quality data. Benko et al (2009) studied this problem by first introducing the functional principal components decomposition along with bootstrap.…”

Section: Introductionmentioning

confidence: 99%

Hypothesis Testing for Multiple Mean and Correlation Curves with Functional Data

Yuan¹,

Fang²,

Li³

et al. 2020

STAT SINICA

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Existing statistical methods of functional data analysis have mostly focused on using local smoothing estimators or some known basis approximations. In many applications with functional observations, the main objectives of statistical inferences are to test (a) the equivalence of a set of unknown mean curves, and (b) the correlation curves of the unknown stochastic processes, while the unknown curves of the functional data may not be approximated by a set of known basis functions. We propose a class of simple to use test statistics, for comparing mean and correlation curves of functional data without relying on the estimation with local smoothing and basis approximations, and studied their basic asymptotic properties. Through an application to the functional gene expression data, we show that our method gives practically meaningful results with minimal assumptions.Numerical justifications of our testing method is provided by a simulation study.

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“…As a nonparametric statistical method, functional data analysis is not limited by a model and its parameters, so it can better reflect real laws in nature. At present, statistical analysis methods for functional data have been widely used in the fields of biology, medicine, economics and meteorology [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Method of L1-Norm Principal Component Analysis for Functional Data

Liu

et al. 2020

Symmetry

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Recently, with the popularization of intelligent terminals, research on intelligent big data has been paid more attention. Among these data, a kind of intelligent big data with functional characteristics, which is called functional data, has attracted attention. Functional data principal component analysis (FPCA), as an unsupervised machine learning method, plays a vital role in the analysis of functional data. FPCA is the primary step for functional data exploration, and the reliability of FPCA plays an important role in subsequent analysis. However, classical L2-norm functional data principal component analysis (L2-norm FPCA) is sensitive to outliers. Inspired by the multivariate data L1-norm principal component analysis methods, we propose an L1-norm functional data principal component analysis method (L1-norm FPCA). Because the proposed method utilizes L1-norm, the L1-norm FPCs are less sensitive to the outliers than L2-norm FPCs which are the characteristic functions of symmetric covariance operator. A corresponding algorithm for solving the L1-norm maximized optimization model is extended to functional data based on the idea of the multivariate data L1-norm principal component analysis method. Numerical experiments show that L1-norm FPCA proposed in this paper has a better robustness than L2-norm FPCA, and the reconstruction ability of the L1-norm principal component analysis to the original uncontaminated functional data is as good as that of the L2-norm principal component analysis.

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Functional ANOVA starting from discrete data: an application to air quality data

Cited by 19 publications

References 30 publications

A Two-Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis

A Two-Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis

Hypothesis Testing for Multiple Mean and Correlation Curves with Functional Data

A Method of L1-Norm Principal Component Analysis for Functional Data

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