To improve the numerical evaluation of integrals in Number-Theoretic Methods, we give a two-stage algorithm. The main idea is that we distribute the points according to the variations of the quadrature on the subdomai...To improve the numerical evaluation of integrals in Number-Theoretic Methods, we give a two-stage algorithm. The main idea is that we distribute the points according to the variations of the quadrature on the subdomains to reduce errors. The simulations results are also given.展开更多
In the present paper approximating functions for certain periodic functions in several variables with bounded mixed derivatives are constructed by making use of their values at the knots of some number-theoretic nets....In the present paper approximating functions for certain periodic functions in several variables with bounded mixed derivatives are constructed by making use of their values at the knots of some number-theoretic nets. The errors are estimated in the L_q-norm where l≤q≤∝.展开更多
THE range of usage of the quadrature formulae specially designed for the integrals of sometypes can often be extended by the variable transformation. For example, in a quadrature for-mula computing an integral with th...THE range of usage of the quadrature formulae specially designed for the integrals of sometypes can often be extended by the variable transformation. For example, in a quadrature for-mula computing an integral with the weight function g:展开更多
This article investigates the test for linearity of a multivariate stochastic regression model.The use of nonparametric regression procedures for developing regression diagnostics has beenthe subject of several recent...This article investigates the test for linearity of a multivariate stochastic regression model.The use of nonparametric regression procedures for developing regression diagnostics has beenthe subject of several recent research efforts. However, when the dimension of the regressor islarge, some traditional nonparametric methods, such as kernel estimation, may be inefficient.We in this article suggest two test statistics based on projection pursuit technique and kernelmethod. The tests proposed are consistent against all fixed smooth alternatives to linearityand are asymptotically distribution-free for the distribution of the error. Furthermore, the testsare applied to an example of real-life data and some simulated data sets to demonstrate theavailability of the tests proposed.展开更多
文摘To improve the numerical evaluation of integrals in Number-Theoretic Methods, we give a two-stage algorithm. The main idea is that we distribute the points according to the variations of the quadrature on the subdomains to reduce errors. The simulations results are also given.
基金This work is supported in part by the Alexander von Humboldt Foundationthe National Natural Science Foundation of China
文摘In the present paper approximating functions for certain periodic functions in several variables with bounded mixed derivatives are constructed by making use of their values at the knots of some number-theoretic nets. The errors are estimated in the L_q-norm where l≤q≤∝.
文摘THE range of usage of the quadrature formulae specially designed for the integrals of sometypes can often be extended by the variable transformation. For example, in a quadrature for-mula computing an integral with the weight function g:
文摘This article investigates the test for linearity of a multivariate stochastic regression model.The use of nonparametric regression procedures for developing regression diagnostics has beenthe subject of several recent research efforts. However, when the dimension of the regressor islarge, some traditional nonparametric methods, such as kernel estimation, may be inefficient.We in this article suggest two test statistics based on projection pursuit technique and kernelmethod. The tests proposed are consistent against all fixed smooth alternatives to linearityand are asymptotically distribution-free for the distribution of the error. Furthermore, the testsare applied to an example of real-life data and some simulated data sets to demonstrate theavailability of the tests proposed.
