This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown ...
详细信息
This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown quantile regression function, whose asymptotic properties are established under quite general conditions. specificationtesting of the quantile regression function is further considered through a statistic constructed based on the integrated squared distance between the parametric and the nonparametric estimators for the regression function. The test statistic is shown to converge to a random variable related to the local time of an Ornstein-Uhlenbeck process under the parametric null. The power of the test against local alternatives is also investigated. Additional asymptotic results on the null parametric quantile estimators and a bootstrap test are developed as well. Numerical results demonstrate that the proposed nonparametric estimator and the specification test enjoy attractive finite sample performance. (C) 2021 Elsevier B.V. All rights reserved.
In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases w...
详细信息
In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator. (C) 1999 Academic Press AMS 1991 subject classifications: 62G07, 62G10, 62J12.
暂无评论