Linear Processes in Function Spaces

By D. Bosq. 2000

680 citations recorded by the source corpus.

Subfields: Information Systems, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3a13c32f3a895d8eccd66c23b1112ed5f879fa07

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Citations in the corpus

Functional data clustering: a survey (2013, background): “…remind the monographs on functional data by Ramsay and Silverman (2002, 2005) developing theory and applications on functional data, the book of Bosq (2000) for modelling dependent functional random variables and the recent book of Ferraty and Vieu (2006) on non-parametric models for…”
Theory for high-order bounds in functional principal components analysis (2009, background): “Lemma 3·4 is implicit in Bosq (1991, 2000).”
Determining the order of the functional autoregressive model (2013, methodology): “1 of Bosq (2000). For ease of reference, we state the following definition.”
Estimation of the mean of functional time series and a two‐sample problem (2011, methodology): “Bosq (2000) studied the theory of linear functional time series, focusing on the functional auto-regressive (FAR) model.”
Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains (2015, background): “(15) guarantees that φ̂( j)m is an estimator for φ ( j) m rather than for −φ( j)m , as eigenfunctions are defined only up to a sign change (Bosq 2000; Hall and Hosseini-Nasab 2006).”
Convolutional autoregressive models for functional time series (2016, neutral): “…out-of-sample forecasting error of X t ( · ) is used to compare the prediction performance of the estimated CFAR(2) model with the FAR model by Bosq (2000) and the functional random walk model, where 4 shows the estimated ρ and σ 2 using the CFAR(2) model, and the mean squared out-sample…”
Testing stationarity of functional time series (2014, methodology): “…7.7 10.8 5.8 .90 8.6 5.3 10.0 4.5 12.1 7.3 10.5 5.4 .95 8.5 4.7 9.8 5.2 11.9 7.1 10.6 5.4 where the W i are independent Brownian motions on [0] [1], and ψ is a kernel whose operator norm is not too large, the precise condition is somewhat technical, see Bosq (2000) Schmidt norm of ψ be less than 1.”
Adaptive functional linear regression (2011, methodology): “…class of estimation procedures of the slope function studied in the statistical literature are based on principal components regression (see e.g. Bosq [2000], Frank and Friedman [1993], Cardot et al. [1999], Cardot et al. [2007] or Müller and Stadtmüller [2005] in the context of generalized…”
Identifying the finite dimensionality of curve time series (2010, background): “Therefore, P (d̂ < d) = P (θ̂d−1 < ǫ) = P (θd−1 − θ̂d−1 > θd−1 − ǫ) (B.25) ≤ P (|θd−1 − θ̂d−1|> θd−1 − ǫ) ≤ P (‖K̂ −K‖S > θd−1 − ǫ), where the final inequality follows from Lemma 4.2 in Bosq (2000).”
Smoothing splines estimators for functional linear regression (2009, methodology): “This situation has been considered, for instance, in Cardot, Ferraty and Sarda [7] and Müller and Stadtmüller [23] for independent variables, while correlated functional variables are studied in Bosq [2].”
Dynamic functional principal components (2012, methodology): “To benefit from increasing information, we need appropriate statistical tools that can help to extract the most important characteristics of some possibly high dimensional specifications.”
DEPENDENT FUNCTIONAL LINEAR MODELS WITH APPLICATIONS TO MONITORING STRUCTURAL CHANGE (2014, neutral): “We refer the interested reader to Bosq (2000) and Gohberg, Golberg, and Kaashoek (1990) for relevant background on random elements in functions spaces and functional analysis, respectively.”
The conditional central limit theorem in Hilbert spaces (2003, methodology): “Other examples are given by Bosq (2000) and Merlev+ede (1995), who study linear processes taking their values in separable Hilbert spaces.”
SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL (2003, methodology): “Such an approach has also been proposed by Bosq (1991, 2000) in order to predict an Hilbertian autoregressive process.”
Testing for stationarity of functional time series in the frequency domain (2017, background): “M E ] 8 O ct 2 may consult Bosq (2000), Ferraty & Vieu (2010), Horváth & Kokoszka (2012), Hsing & Eubank (2015) and Ramsay & Silverman (2005).”
High Dimensional Statistical Inference and Random Matrices (2006, background): “For entries into this literature, see for example [14, 28, 48]”
Nonstationarity in time series of state densities (2016, methodology): “The reader is referred to, e.g., Bosq (2000) for a brief introduction to Hilbertian random variables and the definitions of their moments.”
Asymptotic normality of the principal components of functional time series (2013, background): “This condition clearly holds for the functional autoregressive process with the autoregressive operator Ψ because in that case Ψ j = Ψ j , and Ψ jL ≤ ab j , for some a > 0 and b < 1; see Chapter 3 of [4] or Chapter 13 of [19].”