On weighted U-statistics for stationary processes

By T. Hsing, Wei Biao Wu. 2004

78 citations recorded by the source corpus.

A weighted U-statistic based on a random sample X1;::: ;Xn has the form Un = P 1•i;jn wiijK(Xi;Xj) where K is fixed symmetric measurable function and the wi are symmetric weights. A large class of statistics can be expressed as weighted U-statistics or variations thereof. This paper establishes the asymptotic normality of Un when the sample observations come from a non-linear time series and linear processes. MSC 2000 subject classifications. Primary 60F05; secondary 60G10.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8096d5ec067322ce23082900a06a31379374cfdc

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Citations in the corpus

Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications (2016, background): “When p (and therefore d) is fixed, the classical central limit theorems (CLT) for approximating Tn by a Gaussian random vector T \ n ∼ N(0,Γ), where Γ = Cov(g(X1)) and g(X1) = E[h(X1, X2)|X1] − θ, have been extensively studied in literature [36, 3, 39, 33, 26, 37, 34, 67, 3, 75, 32, 38, 39, 67].”
On linear processes with dependent innovations (2005, background): “The GMC property implies that the process fatg forgets the past F0 exponentially fast in terms of the Euclidean distance between an and its coupled version a 0 n: It is easily verifiable since it is directly related to the data generating mechanism of the process fang: Recently, Hsing and Wu [30] ob”
TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS (2010, methodology): “Further we assume that ut satisfies the geometric-moment contraction (GMC) condition (Hsing and Wu, 2004; Shao and Wu, 2007; Wu and Shao, 2004).”
On the Bahadur representation of sample quantiles for dependent sequences (2005, background): “od and established a central limit theory for stationary processes; see also [14]. Wu and Woodroofe [37] present some recent developments. Several of its applications on various problems are given in [15, 18, 31, 32, 34]. BAHADUR REPRESENTATION 3 Historically many limit theorems for dependent random”
Robust Spectral Analysis (2011, background): “By Lemma 1 of Jansson (2002), the limit superior of B−1 n ∑ |j|<n |w(j/Bn)| is finite, and in view of the assumed Lipschitz continuity, the first term on the right-hand side of the preceding display then vanishes because Bnn −1/2 → 0.”