In this study,we explore the problem of hypothesis testing for white noise in high-dimensional settings,where the dimension of the random vector may exceed the sample sizes.We introduce a test procedure based on spati...In this study,we explore the problem of hypothesis testing for white noise in high-dimensional settings,where the dimension of the random vector may exceed the sample sizes.We introduce a test procedure based on spatial-sign for high-dimensional white noise testing.This new spatial-sign-based test statistic is designed to emulate the test statistic proposed by Paindaveine and Verdebout[(2016).On high-dimensional sign tests.Bernoulli,22(3),1745–1769.],but under a more generalized scatter matrix assumption.We establish the asymptotic null distribution and provide the asymptotic relative efficiency of our test in comparison with the test proposed by Feng et al.[(2022).Testing for high-dimensional white noise.arXiv:2211.02964.]under certain specific alternative hypotheses.Simulation studies further validate the efficiency and robustness of our test,particularly for heavy-tailed distributions.展开更多
基金supported by the National Natural Science Foundation of China(Grants 12101335 and 12271271)the Natural Science Foundation of Tianjin(Grant 21JCQNJC00020)+5 种基金the Fundamental Research Funds for the Central Universities,Nankai University(Grants 63211088,63221050,and 63231013)Wukong Investment Research Fundspartially supported by the China National Key R&D Programunder Grant Nos.2022YFA1003703,2022YFA1003800,and 2019YFC1908502the National Natural Science Foundation of China under Grant Nos.12226007,12271271,11925106,12231011,11931001 and 11971247the Fundamental Research Funds for the Central Universities under Grant No.ZB22000105Shenzhen Wukong Investment Management Co.Ltd.
文摘In this study,we explore the problem of hypothesis testing for white noise in high-dimensional settings,where the dimension of the random vector may exceed the sample sizes.We introduce a test procedure based on spatial-sign for high-dimensional white noise testing.This new spatial-sign-based test statistic is designed to emulate the test statistic proposed by Paindaveine and Verdebout[(2016).On high-dimensional sign tests.Bernoulli,22(3),1745–1769.],but under a more generalized scatter matrix assumption.We establish the asymptotic null distribution and provide the asymptotic relative efficiency of our test in comparison with the test proposed by Feng et al.[(2022).Testing for high-dimensional white noise.arXiv:2211.02964.]under certain specific alternative hypotheses.Simulation studies further validate the efficiency and robustness of our test,particularly for heavy-tailed distributions.
