Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is con...Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.展开更多
The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the author...The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.展开更多
The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential s...The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponen- tially as x → -∞, but it can be arbitrarily large in other locations.展开更多
For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables...For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.展开更多
Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equati...Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.展开更多
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.
基金Project supported by the National Natural Science Foundation of China(Nos.10871175,10931007)the Zhejiang Provincial Natural Science Foundation of China(No.Z6100217)
文摘The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.
文摘The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponen- tially as x → -∞, but it can be arbitrarily large in other locations.
基金supported by the National Natural Science Foundation of China under Grant No.11101396the State Key Program of National Natural Science of China under Grant No.11231010the Fundamental Research Funds for the Central Universities under Grant No.WK2040000010
文摘For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.
文摘Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.
