Checking Heteroscedasticity in Partially Linear Single-Index Models Using Pairwise Distance

Autor: Jian-Qiang Zhao, Jianquan Li, Yan-Yong Zhao, Junyan He, Waled Khaled
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: IEEE Access, Vol 8, Pp 25286-25298 (2020)
Druh dokumentu: article
ISSN: 2169-3536
DOI: 10.1109/ACCESS.2020.2970506
Popis: In this article, a new test is proposed for partially linear single-index models (PLSIM) based on the pairwise distances of the sample points, to test heteroscedasticity. The statistic can be formulated as a U statistic and does not have to estimate the conditional variance function by using nonparametric methods, such as kernel, local polynomial, or spline. We derive a computationally feasible approximation to deal with the complexity of the limit zero distribution under the null hypothesis. We prove that the proposed bootstrap procedure is valid approximation to the null distribution of the test. It shows that this statistic has an asymptotically normal distribution. The algorithmic program of this test method is easy to implement and has faster convergence than some existing methods. In addition, convergence rate of the statistic does not depend on the dimensions of the covariates, which greatly reduces the impact of the dimensional curse. Finally, we give the numerical simulations and a real data example.
Databáze: Directory of Open Access Journals