Weak invariance principles for sums of dependent random functions

By István Berkes, Lajos Horv'ath, Gregory Rice. 2013

71 citations recorded by the source corpus.

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.

Subfields: Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4c24f1f41569ebd1346fae010e0998bd0ddc479b

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Citations in the corpus

Convolutional autoregressive models for functional time series (2016, unknown): “Bosq (2000), including Hörmann and Kokoszka (2010), Horváth et al. (2010), Aue et al. (2012), Horváth and Kokoszka (2012), Horváth et al. (2012), Berkes et al. (2013), and Hörmann et al. (2013).”
Long-Range Dependent Curve Time Series (2020, unknown): “Our main focus is on the cases k = 1, . . . , κ0 for which Tnk is constructed using the functional long-range dependent process Xtk, as limit theorems for Tn,κ0+1 have been extensively studied (see, e.g., Bosq 2000; Berkes, Horváth, and Rice 2013).”
Testing stationarity of functional time series (2014, methodology): “The proof of Theorem 2.1 is based on an approximation developed in Berkes et al. (2013) where W i are independent and identically distributed Wiener processes (standard Brownian motions).”
Functional data analysis in the Banach space of continuous functions (2017, background): “[8] Istvn Berkes, Lajos Horvth, and Gregory Rice.”
Testing relevant hypotheses in functional time series via self‐normalization (2018, background): “2) avoids the consistency problem mentioned in Berkson (1938), that is: any consistent test will detect any arbitrary small change in the parameters if the sample size is sufficiently large.”