Limiting behavior of U-statistics for stationary, absolutely regular processes

By K. Yoshihara. 1976

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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.”
Asymptotic theory for stationary processes (2011, background): “Yoshihara (1976), Denker and Keller (1983, 1986), Borovkova, Burton and Dehling (1999, 2001, 2002) and Dehling, Wendler (2010) dealt with strong mixing processes.”
Limit theorems for functionals of mixing processes with applications to U-statistics and dimension estimation (2001, background): “Lemma 4.1 (Yoshihara).”
The treatment-effect estimation: A case study of the 2008 economic stimulus package of China (2015, methodology): “By following the proof arguments as in Fan and Li (1999), i.e., using lemma 1 of Yoshihara (1976), one can show that E(A1n,0) = E(Ã1n,0) + (s.o.) and V ar(A1n,0) = V ar(Ã1n,0) + (s.o.), where Ã1n,0 is defined as in A1n,0 except that (z1t, z2t) are replaced by (z̃1t, z̃2t) wherever they occur.”
Asymptotics for panel quantile regression models with individual effects (2012, methodology): “Suppose that the conditions of Proposition C.1 are satisfied.”
A CONSISTENT NONPARAMETRIC TEST FOR CAUSALITY IN QUANTILE (2012, methodology): “Finally conditions (A2)(d) and (e) are adopted from conditions of Lemma 3.2 of Yoshihara (1976), which are required to get the asymptotic equivalence of the nondegenerate U -statistic and its projection under the β-mixing process.”
A Consistent Characteristic-Function-Based Test for Conditional Independence (2003, methodology): “All lemmas can be proved by using Lemma 1 of Yoshihara (1976) repeatedly.”
Nonparametric Lag Selection for Time Series (2000, methodology): “…the local constant estimator f̂ 1(x) is used instead, then E[(II9)2w( ~X M , t)] c(h)C1 Ofh4(nÿ im 1)ÿ1=2g: The term E(I9II 9w( ~X M , t)) is negligible by a standard U-statistic argument, using our betamixing assumption (A1) and Lemma 1 of Yoshihara (1976), similar to Tjùstheim and Auestad (1994).”
Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to ExtremeValue Data (2000, methodology): “…the variance that would arise in the case of independent data, and B represents cross-product terms arising on account of correlation; (iii) using methods of Yoshihara (1976) to bound B by a quantity that, in view of our condition (a), equals o νh as ν → ∞ and (iv) using elementary calculus to…”
A semiparametric GARCH model for foreign exchange volatility (2006, methodology): “Applying again the Lemmas 2 and 3 of Yoshihara (1976), one obtains that Z = Op ( n−1h−1/2 ) = op ( n−1/2 ) .”
Tests for changing mean with monotonic power (2009, unknown): “(Lemma 1, Yoshihara (1976)) Let xt1 , xt2 , . . . , xtk (with t1 t2 · · · tk) be absolutely regular random vectors with mixing coefficients β.”
Smoothed quantile regression for panel data (2015, unknown): “Since |z̄it| is uniformly bounded by some constant depending only on K(·), by the exponential β-mixing property (condition (A1)) and Theorem 3 of Yoshihara (1978), it is shown that the first term on (A.”
Testing Conditional Independence Via Empirical Likelihood (2014, methodology): “Yoshihara (1989) proved the above lemma for the β-mixing case.”