Analysis of Variance for Functional Data

Zhang, Jin‐Ting

doi:10.1201/b15005

Cited by 171 publications

(151 citation statements)

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“…In FANOVA for two functional samples with a common covariance function one wishes to test the null hypothesis of equality of mean functions versus the alternative hypothesis that the mean functions are different [37]. Our approach is exemplified by activity data obtained experimentally for a small neotropical marsupial, Gracilinanus microtarsus.…”

Section: Introductionmentioning

confidence: 99%

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Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis

Henning¹,

Kist²,

Pinheiro³

et al. 2017

OJS

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Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.

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Section: Introductionmentioning

confidence: 99%

“…we will use functional analysis of variance (FANOVA), which is the equivalent of ANOVA for functional data [37]. In FANOVA for two functional samples with a common covariance function one wishes to test the null hypothesis of equality of mean functions versus the alternative hypothesis that the mean functions are different [37].…”

Section: Introductionmentioning

confidence: 99%

Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis

Henning¹,

Kist²,

Pinheiro³

et al. 2017

OJS

View full text Add to dashboard Cite

show abstract

“…The wavelet transform of the data is again used in the implementation of this approach (see also [4]). Recently, in the context of functional data defined by curves, considering the L 2 -norm, an up-to-date overview of hypothesis testing methods for functional data analysis is provided in [62], including functional ANOVA, functional linear models with functional responses, heteroscedastic ANOVA for functional data, and hypothesis tests for the equality of covariance functions, among other related topics.…”

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confidence: 99%

The effect of the spatial domain in FANOVA models with ARH(1) error term

Álvarez-Liébana

Ruiz-Medina

2017

Statistics and Its Interface

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SummaryFunctional Analysis of Variance (FANOVA) from Hilbert-valued correlated data with spatial rectangular or circular supports is analyzed, when Dirichlet conditions are assumed on the boundary. Specifically, a Hilbertvalued fixed effect model with error term defined from an Autoregressive Hilbertian process of order one (ARH (1) process) is considered, extending the formulation given in [51]. A new statistical test is also derived to contrast the significance of the functional fixed effect parameters. The Dirichlet conditions established at the boundary affect the dependence range of the correlated error term. While the rate of convergence to zero of the eigenvalues of the covariance kernels, characterizing the Gaussian functional error components, directly affects the stability of the generalized least-squares parameter estimation problem. A simulation study and a real-data application related to fMRI analysis are undertaken to illustrate the performance of the parameter estimator and statistical test derived.

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“…Cuevas [3] and Horvàth and Kokoska [12] and Zhang's [37] books provide an up-to-date state of the art in functional data analysis and complement the reference books [20] and [7]. Applications of functional data analysis can be found in various scientific areas, including climatological and environmental ones (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Modelling collocation uncertainty of 3D atmospheric profiles

Ignaccolo

Franco‐Villoria

Fassò

2014

Stoch Environ Res Risk Assess

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Atmospheric thermodynamic data are gathered by high technology remote instruments such as radiosondes, giving rise to profiles that are usually modelled as functions depending only on height. The radiosonde balloons, however, drift away in the atmosphere resulting in not necessarily vertical but threedimensional (3D) trajectories. To model this kind of functional data, we introduce a "point based" formulation of an heteroskedastic functional regression model that includes a trivariate smooth function and results to be an extension of a previously introduced unidimensional model. Functional coefficients of both the conditional mean and variance are estimated by reformulating the model as a standard generalized additive model and subsequently as a mixed model. This reformulation leads to a double mixed model whose parameters are fitted by using an iterative algorithm that allows to adjust for heteroskedasticity. The proposed modelling approach is applied to describe collocation mismatch when we deal with couples of balloons launched at two

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Analysis of Variance for Functional Data

Cited by 171 publications

References 0 publications

Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis

Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis

The effect of the spatial domain in FANOVA models with ARH(1) error term

Modelling collocation uncertainty of 3D atmospheric profiles

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