Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decom...Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.展开更多
The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD...The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.展开更多
基金supported by National Natural Science Foundation of China (GrantNos.10931002,10911120386)
文摘Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.
基金supported by National Science Fund of Distinguished Young Scholars of China(Grant No. 40725012)40821002)National Natural Science Foundation of China (Grant No. 41074073)
文摘The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.
