A simple multiway ANOVA for functional data

Cuesta-Albertos, Juan A.; Febrero–Bande, Manuel

doi:10.1007/s11749-010-0185-3

Cited by 95 publications

(48 citation statements)

References 27 publications

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“…To reduce the error introduced by the choice of the random projection, we will use the correction that implies controlling the false discovery rate (FDR) introduced by Benjamini and Hochberg (1995) [26]. This method is also recommended by Cuesta-Albertos and Febrero-Bande [20]. In particular, we use the FDR procedure that arises from the work of Benjamini and Yakutieli (2001) [27].…”

Section: Methodsmentioning

confidence: 99%

Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis

et al. 2014

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BackgroundPairwise association between neurons is a key feature in understanding neural coding. Statistical neuroscience provides tools to estimate and assess these associations. In the mammalian brain, activating ascending pathways arise from neuronal nuclei located at the brainstem and at the basal forebrain that regulate the transition between sleep and awake neuronal firing modes in extensive regions of the cerebral cortex, including the primary visual cortex, where neurons are known to be selective for the orientation of a given stimulus. In this paper, the estimation of neural synchrony as a function of time is studied in data obtained from anesthetized cats. A functional data analysis of variance model is proposed. Bootstrap statistical tests are introduced in this context; they are useful tools for the study of differences in synchrony strength regarding 1) transition between different states (anesthesia and awake), and 2) affinity given by orientation selectivity.ResultsAn analysis of variance model for functional data is proposed for neural synchrony curves, estimated with a cross-correlation based method. Dependence arising from the experimental setting needs to be accounted for. Bootstrap tests allow the identification of differences between experimental conditions (modes of activity) and between pairs of neurons formed by cells with different affinities given by their preferred orientations. In our test case, interactions between experimental conditions and preferred orientations are not statistically significant.ConclusionsThe results reflect the effect of different experimental conditions, as well as the affinity regarding orientation selectivity in neural synchrony and, therefore, in neural coding. A cross-correlation based method is proposed that works well under low firing activity. Functional data statistical tools produce results that are useful in this context. Dependence is shown to be necessary to account for, and bootstrap tests are an appropriate method with which to do so.

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Section: Methodsmentioning

confidence: 99%

Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis

et al. 2014

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“…is minimized, with, as before, Λ −1 k defining the inverse of matrix Λ k given in (14) (and approximated by Λ k , when R 0 and R 1 are unknown). That is,…”

Section: /2mentioning

confidence: 99%

“…Here, for each k ≥ 1, Λ k is defined in (14). The functional components of variance associated with the transformed model (24) are then given by…”

Section: /2mentioning

confidence: 99%

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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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“…Since we are dealing with functional data (the L-functions), we choose to use the method proposed in [13]. Basically, this method uses random projections to transform functional data into univariate data and then solves the obtained simple scalar ANOVA problem.…”

Section: ) Analysis Of Variance For Functional Datamentioning

confidence: 99%

Comparison of the spatial organization in colorectal tumors using second-order statistics and functional ANOVA

Aliy

Séguin

Fischer

et al. 2013

2013 8th International Symposium on Image and Signal Processing and Analysis (ISPA)

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Abstract-We propose an automatic method to quantitatively describe the spatial organization governing populations of biological objects, such as cells, which exist in stationary histology images. This quantification is of prime importance when striving to compare different tumoral models in order to evaluate potential therapies. We compare two animal models of colorectal cancer. Our approach is based on the topographic map to automatically extract the location of the relevant biological objects. We describe their spatial organization along a continuous range of scales using second-order statistics. Using a functional analysis of variance test, we show that there are significant differences in these statistics depending on cancer model, and on the day after tumor implant.

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A simple multiway ANOVA for functional data

Cited by 95 publications

References 27 publications

Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis

Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis

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

Comparison of the spatial organization in colorectal tumors using second-order statistics and functional ANOVA

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