On U-statistics and v. mise’ statistics for weakly dependent processes

By Manfred Denker, Gerhard Keller. 1983

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Citations in the corpus

Basic properties of strong mixing conditions. A survey and some open questions (2005, methodology): “wn by Peligrad [124] with an extension of the arguments used by Cogburn [57] and Ibragimov [91] to show the inequality ρ(A,B) ≤ 2[φ(A,B)]1/2 (see also Doob [70, p. 222, Lemma 7.1]). Denker and Keller [65] independently proved the similar inequality ρ(A,B) ≤ 2 · max{φ(A,B),φ(B,A)}. Equation (1.18) es”
A Kernel Loss for Solving the Bellman Equation (2019, background): “…provide consistent estimation of the expected quadratic quantity given the sample is weakly dependent and satisﬁes certain mixing condition (e.g., Denker & Keller, 1983; Beutner & Z¨ahle, 2012); this often amounts to saying that { s i } forms a Markov chain that converges to its stationary…”
The Jackknife and the Bootstrap for General Stationary Observations (1989, background): “In the examples above rigorous conditions can be found in Gastwirth and Rubin (1975) for i), Denker and Keller (1983) for iii), Bustos (1982) and Tjostheim (1986) for iv).”
A test for independence based on the correlation dimension (1996, methodology): “Cm;n in equation (2.2) is a generalized U-statistic (c.f., Ser ing (1980, Chapter 5), and Denker and Keller (1983)) with symmetric kernel (kx yk).”
THE LAW OF LARGE NUMBERS FOR U{STATISTICS UNDER ABSOLUTE REGULARITY (1998, background): “Sen (1972), Yoshihara (1976) and Denker and Keller (1983) proved a central limit theorem and a law of the iterated logarithm for U–statistics under different types of dependence conditions.”
Nonparametric Tests for Serial Independence Based on Quadratic Forms (2005, unknown): “It follows from the results by Denker and Keller (1983) that under strict stationarity and absolute regularity, the proposed tests for serial independence are consistent against all fixed alternatives. In contrast to some other tests based on quadratic functionals, such as that of Székely and Rizzo ”
A new statistic and practical guidelines for nonparametric Granger causality testing (2006, background): “According to Denker and Keller (1983), Tn is asymptotically N(μ, σ 2 n ) distributed, with μ = (2 )XY +dZ q̃ and”
Asymptotic theory for stationary processes (2011, background): “Asymptotic properties for kernel estimates of iid observations have been studied in Silverman (1986), Devroye and Györfi (1985), Wand and Jones (1995), Prakasa Rao (1983), Nadaraya (1989) and Eubank (1999) among others, and for strong mixing processes in Robinson (1983), Singh and Ullah (1985), Cast”
How strong are the causal relationships between Islamic stock markets and conventional financial systems? Evidence from linear and nonlinear tests (2014, methodology): “The asymptotic variance σ2(m,Ly, Le, ) is estimated using the theory of U-statistic for weakly dependent processes (Denker and Keller, 1983).6 The test statistic in Eq.”
Copula goodness-of-fit testing: an overview and power comparison (2009, methodology): “Each term of this decomposition is estimated using V-statistics (see Denker and Keller 1983 ) for an introduction to U- and V-statistics).”
Goodness-of-fit test for copulas (2005, methodology): “Relying on the theory of V-statistics it is also possible to develop asymptotics [ 10 ] for the functionalof interest Q.”
Nonlinear Granger Causality: Guidelines for Multivariate Analysis (2013, unknown): “Following the Diks and Panchenko (2006) methodology, this implies that the sum of dominating squared terms in Eq.”