Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data

Aneiros, Germán; Vieu, Philippe

doi:10.1007/s11749-015-0471-1

Cited by 11 publications

(5 citation statements)

References 24 publications

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“…At the opposite of the pure additive multi‐functional nonparametric model ) is the naive additive linear model which is constructed by assuming that each component in ) the same linear form as in ). Most recent advances for this model can be found in Aneiros and Vieu (2016b), including asymptotic normality and confidence prediction intervals for the case when Y can also be functional. Of course this linear approach suffers from the same drawbacks as for the case of a single functional covariate (see discussion before), and there is again the need for developing new models being intermediary between linear and nonparametric ones. A multiple index type model .…”

Section: Dimension Reduction For Multifunctional Covariatementioning

confidence: 99%

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On semiparametric regression in functional data analysis

Ling

Vieu

2020

WIREs Computational Stats

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The aim of this paper is to provide a selected advanced review on semiparametric regression which is an emergent promising field of researches in functional data analysis. As a deliberate strategy, we decided to focus our discussion on the single functional index regression (SFIR) model in order to fix the ideas about the stakes linked with infinite dimensional problems and about the methodological challenges that one has to solve when building statistical procedure: one of the most challenging issue being the question of dimensionality effects reduction. This will be the first (and the main) part of this discussion and a complete survey of the literature on SFIR model will be presented. In a second attempt, other semiparametric models (and more generally, other dimension reduction models) will be shortly discussed with the double goal of presenting the state of art and of defining challenging tracks for the future. At the end, we will discuss how additive modeling is an appealing idea for more complicated models involving multifunctional predictors and some tracks for the future will be pointed in this setting. This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

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Section: Dimension Reduction For Multifunctional Covariatementioning

confidence: 99%

“…

Y = g_{1} ((), 〈θ_{1}, Δ^{1}〉) + \dots + g_{p} ((), 〈θ_{p}, Δ^{p}〉) + ε,

has been studied in Aneiros and Vieu (2016b). Statistical inference developed in this paper shows that, without surprise, any component g j (.)…”

Section: Dimension Reduction For Multifunctional Covariatementioning

confidence: 99%

On semiparametric regression in functional data analysis

Ling

Vieu

2020

WIREs Computational Stats

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“…Sparsity effects are related to the dimension of the variables in the sample, and for this reason they appear under many guises in FDA; see [12] for a broad discussion on sparsity in FDA settings. In this Special Issue, sparsity issues arise within each functional observation in contribution [79] and through the model in contribution [18].…”

Section: Sparsity In Fdamentioning

confidence: 99%

Recent advances in functional data analysis and high-dimensional statistics

Aneiros

Cao

Fraiman

et al. 2019

Journal of Multivariate Analysis

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124

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“…Generally, there are many different concepts of sparsity and we refer to Aneiros and Vieu (2016) for a comprehensive overview. Throughout this paper, we use the terms sparse and dense in order to differentiate between the following two asymptotic scenarios: sparse: m/n 1/5 → 0 and dense: m/n 1/5 → ∞, where the value 1/5 of the exponent is determined by our theory.…”

Section: Introductionmentioning

confidence: 99%

Inference for sparse and dense functional data with covariate adjustments

Liebl

2019

Journal of Multivariate Analysis

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We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted functional data -depending on the relative order of m (the discretization points per function) and n (the number of functions). Our simulation results demonstrate that the existing asymptotic normality results can lead to severely misleading inferences in finite samples. We explain this phenomenon based on our theoretical results and propose finite-sample corrections which provide practically useful approximations for inference in sparse and dense data scenarios. The relevance of our theoretical results is showcased using a real-data application.

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Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data

Cited by 11 publications

References 24 publications

On semiparametric regression in functional data analysis

On semiparametric regression in functional data analysis

Recent advances in functional data analysis and high-dimensional statistics

Inference for sparse and dense functional data with covariate adjustments

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