An introduction to recent advances in high/infinite dimensional statistics

Goia, Aldo; Vieu, Philippe

doi:10.1016/j.jmva.2015.12.001

Cited by 197 publications

(70 citation statements)

References 80 publications

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“…In fact, because of both the wide scope of applied problems related to that kind of data and the various methodological challenges that the mathematical community has to face, functional data analysis (FDA) became This comment refers to the invited paper available at: doi:10.1007/s11749-015-0470-2. Davidian et al 2004) or Journal of Multivariate Analysis (see Goia and Vieu 2015 for the latest one).…”

Section: A Short Historical Discussion On Sparsitymentioning

confidence: 99%

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

Aneiros

Vieu

2016

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Section: A Short Historical Discussion On Sparsitymentioning

confidence: 99%

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

Aneiros

Vieu

2016

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“…Therefore, under (22), sup j∈{1,...,k n } φ n, j − φ ′ n, j B → a.s. 0, as n → ∞. Let us know consider the projection operators defined, for all x ∈ B ⊂ H, by…”

Section: Lemmamentioning

confidence: 96%

Strongly consistent autoregressive predictors in abstract Banach spaces

Ruiz-Medina

Álvarez-Liébana

2019

Journal of Multivariate Analysis

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This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the component-wise estimator of the autocorrelation operator in the norm of the space L(B) of bounded linear operators on B. The strong consistency of the associated plug-in predictor then follows in the B-norm. A Gelfand triple is defined through the Hilbert space constructed in Kuelbs' lemma [25]. A Hilbert-Schmidt embedding introduces the Reproducing Kernel Hilbert space (RKHS), generated by the autocovariance operator, into the Hilbert space conforming the Rigged Hilbert space structure. This paper extends the work of Bosq [10] and Labbas and Mourid [26].

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“…An important example of big data with high dimensional observations are functional data. Functional Data Analysis (FDA) deals with objects of infinite dimension and problem related with this functional nature are sometimes similar those associated with big data (see, e.g., Ahmed (2017); Goia and Vieu (2016)). In particular, a very relevant question in functional data analysis is dimension reduction (see Vieu (Vieu)).…”

Section: Velocitymentioning

confidence: 99%

Data learning from big data

Torrecilla

Romo

2018

Statistics & Probability Letters

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Technology is generating a huge and growing availability of observations of diverse nature. This big data is placing data learning as a central scientific discipline. It includes collection, storage, preprocessing, visualization and, essentially, statistical analysis of enormous batches of data. In this paper, we discuss the role of statistics regarding some of the issues raised by big data in this new paradigm and also propose the name of data learning to describe all the activities that allow to obtain relevant knowledge from this new source of information.

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An introduction to recent advances in high/infinite dimensional statistics

Cited by 197 publications

References 80 publications

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

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

Strongly consistent autoregressive predictors in abstract Banach spaces

Data learning from big data

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