Introduction to Functional Data Analysis

Kokoszka, Piotr; Reimherr, Matthew

doi:10.1201/9781315117416

Cited by 345 publications

(256 citation statements)

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“…A unit observation is a curve, say X i ( t ), t ∈. For example, X i ( t ) can be the pollution level, at some location, at time t of day i ; numerous examples are given in the books of Horváth and Kokoszka and Kokoszka and Reimherr . Many procedures for functional data require that, or are simplified if, the curves can be assumed to be realizations of a Gaussian random process.…”

Section: Introductionmentioning

confidence: 99%

Testing Normality of Functional Time Series

Górecki

Hörmann

Horváth

et al. 2017

Journal Time Series Analysis

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We develop tests of normality for time series of functions. The tests are related to the commonly used Jarque–Bera test. The assumption of normality has played an important role in many methodological and theoretical developments in the field of functional data analysis. Yet, no inferential procedures to verify it have been proposed so far, even for i.i.d. functions. We propose several approaches which handle two paramount challenges: (i) the unknown temporal dependence structure and (ii) the estimation of the optimal finite‐dimensional projection space. We evaluate the tests via simulations and establish their large sample validity under general conditions. We obtain useful insights by applying them to pollution and intraday price curves. While the pollution curves can be treated as normal, the normality of high‐frequency price curves is rejected.

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Section: Introductionmentioning

confidence: 99%

Testing Normality of Functional Time Series

Górecki

Hörmann

Horváth

et al. 2017

Journal Time Series Analysis

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“…Functional Principal Component Analysis (FPCA) is well suited for data sparsely observed (Yao et al, 2005;Wang et al, 2015). This application was first inspired by the theoretical framework for sparse functional data analysis (S-FDA) described in (Kokoszka and Reimherr, 2017). It is important to note that smoothing is not applied to individual coverage profiles, but smoothing in S-FDA is based on pooling information from N cells.…”

Section: Methodology and Resultsmentioning

confidence: 99%

Sparse functional data analysis accounts for missing information in single-cell epigenomics

Madrigal

Dai

Hadjipantelis

2018

Preprint

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Single-cell epigenome assays produce sparsely sampled data, leading to coverage pooling across cells to increase resolution. Imputation of missing data using deep learning is available but requires intensive computation, and it has been applied only to DNA methylation obtained by single cell bisulfite sequencing. Here, sparsity in chromatin accessibility obtained by scNMT-seq is addressed using functional data analysis to fit sparsely sampled GpC coverage profiles of individual cells taking into account all the cells of the same cell-type or condition. For that, sparse functional principal component analysis (S-FPCA) is applied, and the principal components are used to estimate chromatin accessibility coverage in individual cells. This methodology can potentially be used with other single-cell assays with missing data such as scBS-seq, scNOME-seq, or scATAC-seq. The R package fdapace is available in CRAN, and R code used in this manuscript can be found at: http://github.com/pmb59/sparseSingleCell.

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“…This is just the usual basis expansion step, see e.g. Chapter 3 of Ramsay et al or Chapter 1 of Kokoszka and Reimherr . We thus work in a finite‐dimensional space

H_{K} = sp ({}, B_{1}, B_{2}, ⋯, B_{K})

.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Klepsch et al . Other examples are given in the books by Horváth and Kokoszka and Kokoszka and Reimherr . The theory and methodology of FTS forms a subfield of functional data analysis (FDA).…”

Section: Introductionmentioning

confidence: 99%

Principal Components Analysis of Periodically Correlated Functional Time Series

Kidziński

Kokoszka

Jouzdani

2018

Journal Time Series Analysis

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Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic operator‐valued filters, score processes, and the inversion formulas. We show that these objects are defined via a convergent series under a simple condition requiring summability of the Hilbert–Schmidt norms of the filter coefficients and that they possess optimality properties. We explain how the Hilbert space theory reduces to an approximate finite‐dimensional setting which is implemented in a custom‐build |R| package. A data example and a simulation study show that the new methodology is superior to existing tools if the functional time series exhibits periodic characteristics.

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Introduction to Functional Data Analysis

Cited by 345 publications

References 0 publications

Testing Normality of Functional Time Series

Testing Normality of Functional Time Series

Sparse functional data analysis accounts for missing information in single-cell epigenomics

Principal Components Analysis of Periodically Correlated Functional Time Series

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