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
In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergen...In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.展开更多
In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit techni...In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.展开更多
In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enh...In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.展开更多
基金supported by a NSF grant from National Natural Science Foundation of China(10701035)ChenGuang project of Shanghai Education Development Foundation(2007CG33).
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).
文摘In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.
文摘In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.
基金supported by a grant from the Research Grants Council of Hong Kong.Jianhong Wu was also supported by a grant from Humanities & Social Sciences in Chinese University (07JJD790154)the Youth Talent Foundation of Zhejiang GongShang University (Q09-12)
文摘In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.
