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Quantile inference for nonstationary processes with infinite variance innovations

Applied Mathematics:A Journal of Chinese Universities 2021年第3期36卷 443-461页

作者： LIU Qi-meng LIAO Gui-li ZHANG Rong-mao Department of Mathematics Zhejiang University

Based on the quantile regression, we extend Koenker and Xiao(2004) and Ling and McAleer(2004)'s works from finite-variance innovations to infinite-variance innovations.A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper. It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge. The finite sample studies show that the proposed t-ratio test always performs significantly better than the conventional unit-root tests based on least squares procedure, such as the Augmented Dick fuller(ADf) and Philliphs-Perron(PP) test, in the sense of power and size when infinitevariance disturbances exist. Also, quantile Kolmogorov-Smirnov(QKS) statistic and quantile Cramer-von Mises(QCM) statistic are considered, but the finite sample studies show that they perform poor in power and size, respectively. An application to the Consumer Price Index for nine countries is also presented.

关键词： quantile inference infinite variance α -stable process unit-root t -ratio statistic 62f03 62f05 62f12

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Asymptotic distributions of non-central studentized statistics

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Science China Mathematics 2009年第6期52卷 1262-1284页

作者： SHAO QiMan ZHANG RongMao Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong Department of Mathematics Zhejiang UniversityHangzhou 310027China

Let X 1, ..., X n be independent and identically distributed random variables and W n = W n (X 1, ..., X n ) be an estimator of parameter ?. Denote T n = (W n ? ? 0)/s n , where s n 2 is a variance estimator of W n . In this paper a general result on the limiting distributions of the non-central studentized statistic T n is given. Especially, when s n 2 is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted χ 2 distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.

关键词： non-central studentized statistics studentized U-statistics studentized L-statistics limiting distributions power of tests 62E20 62f05 60f05

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Inference of change-point in single index models

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Science China Mathematics 2008年第10期51卷 1855-1870页

作者： CAO GuanQun WANG Zhanfeng WU YaoHua ZHAO LinCheng Department of Statistics and finance University of Science and Technology of ChinaHefei 230026China

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.

关键词： change point single index models density weighted average derivatives U-statistic Brownian bridges 62f05 62G05

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Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter

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Science China Mathematics 2008年第10期51卷 1871-1882页

作者： QIN YongSong LEI QingZhu School of Mathematical Sciences Guangxi Normal UniversityGuilin 541004China

This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modifi... 详细信息

关键词： mixture model modified likelihood ratio test asymptotic distribution 62f03 62f05

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