In this note, a sort of partially linear models, Y=βtX+g(T)+εis considered, where T and X are, respectively, one-dimensional and d-dimen-sional, and independent each other. Under the least restrictions for the distr...In this note, a sort of partially linear models, Y=βtX+g(T)+εis considered, where T and X are, respectively, one-dimensional and d-dimen-sional, and independent each other. Under the least restrictions for the distributions of X and ε, a strong consistent estimate of parameter β based on the method of An and Zhu is proposed, and under mild conditions, an estimate of g(T) is proved to be consistent to g(T).展开更多
For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not ...For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.展开更多
文摘In this note, a sort of partially linear models, Y=βtX+g(T)+εis considered, where T and X are, respectively, one-dimensional and d-dimen-sional, and independent each other. Under the least restrictions for the distributions of X and ε, a strong consistent estimate of parameter β based on the method of An and Zhu is proposed, and under mild conditions, an estimate of g(T) is proved to be consistent to g(T).
基金the National Natural Science Foundation of China and a CRGC grant of The University of Hong Kong.
文摘For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.
