$NA$ 相依样本部分线性模型估计理论

考虑部分线性模型 ,其中误差为NA相依样本,具有公共未知分布函数G(·),卢为未知参数, g(·)为未知函数.本文首先建立β和g(·)的相合性估计βn和gn(·),然后基于βn和gn(·)构造出G(·)的非参数估计Gn(·),最后在适当条件下,建立了Gn(·)一致强相合于G(·).     

相依样本非参数回归模型误差的相合估计

考虑非参数回归模型Y_i=g(X_i) c_i,i=1,2,…,其中误差㈦)为吵混合随机变量序列且具有公共的未知密度f(·),g(x)=E(Y|X=t)为未知回归函数。本文首先基于g(·)的非参数估计l(x)定义残差,然后基于残差构造f(·)的估计l(x),最后在适当条件下建立l(x)的逐点相合性及一致强相合性。     

强相依数据的函数系数部分线性模型的估计

本文讨论在数据是强相依的情况下函数系数部分线性模型的估计．首先,采用局部线性方法,给出该模型函数项函数的估计;然后,使用两阶段方法给出系数函数的估计．并且讨论了函数项函数估计的渐近正态性,以及系数函数估计的弱相合性和渐近正态性.模拟研究显示,这些估计是较为理想的．     

弱相依误差线性回归模型M-估计的弱相合性

本文考虑线性回归模型yi=xTiβ+ei,i=1,2,…,n,其中ei是(ε,ψ)-弱相依随机误差.在较一般的条件下,我们得到了M-估计弱相合性的统一结果,该结果推广了线性回归模型M-估计的相应结论,包括所有时间序列相依误差,如:高斯序列、相协序列、Bernoulli漂移、Markov链、一些广泛使用的线性或非线性时间...     

矩阵损失下一类相依回归模型中的线性容许估计和Minimax估计

本文研究设计矩人有相同值域的相依回归模型,在矩阵损失下我们给出了回归系数的线性估计是线性容许的充要条件,它们推广了已有的结果,我们也在矩阵上给出了某个回归模型的回归系数的唯一的Ｍｉｎｉｍａｘ估计,它说明此时其它模型的信息不起作用     

相依线性回归系统回归系数的预检验岭估计

对于由两个相依线性回归方程组成的线性回归系统，文「５」提出了基于最小二乘估计和协方差改进估计的一种新型估计，即预检验估计，它具有许多优良性质，但是在设计阵呈病态时，预检验估计的均方误差很大，因而在这种情况下不再被谯是良好估计。     

部分线性回归模型中的自适应估计

考虑半参数回归模型y_i=x_iβ+g(t_i)+e_i,1≤i≤n;其中g(·)是未知函数,β是待估参数,e_i是随机误差. 本文首先在(x_i,t_i)是i.i.d设计点列下,当g(·)的估计取一类核估计序列时,构造了β的自适应估计β_n,同时给出了β_n及g_n^*(g的最终估计)的渐近最优强弱收敛速度;然后在(x_i,t_i)是固定非随机设计点列下,当g(·)的估计取一般非参数估计(包括常见核估计和近邻估计),讨论了β的最小二乘估计的渐近正态性.     

NA相依样本下固定设计非参数回归权函数估计

在NA相依样本下,研究固定设计非参数回归权函数估计的强相合性和完全收敛性,获得了一些较合理的充分条件,较好地推广和改进了Georgiev在独立情形下所得到的相应结论。     

线性模型中误差为相依情形下误差方差估计的Berry—Esseen界限

本文主要讨论了线性模型中误差为α－混合强一稳序列情形下，误差方差估计的Ｂｅｒｒｙ－Ｅｓｓｅｅｎ界限，其阶为ｎ＾－１／２＋λ。     

部分线性自回归模型中误差方差伪最小二乘估计的渐近正态性

Consider the model Y_t=βY_t-1 g(Y_(t-2)) ε_t for 3＜=t＜=T.Here g is an unknown function,βis an unknown parameter,ε_t are i.i.d,random errors with mean 0 and varianceσ~2 and the fourth momentα_4,andε_t are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators■_T~2,■4T and■_T~2 ofσ~s,α_4 and Var(ε_3~2)are respectively constructed based on piecewise polynomial approximator of g.The weak consistency of■4T and■_T~2 are proved.The asymptotic normality of■_T~2 is given,i.e.T~(1/2)(■_T~2-σ~2)/■_T converges in distribution to N(0,1).The result can be used to establish large sample interval estimates ofσ~2 or to make large sample tests forσ~2.     

Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors

Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process.     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.     

非参数计量经济联立模型的局部线性两阶段最小二乘估计

联立方程模型在经济政策制定，经济结构分析和经济预测方面起重要作用，本在随机设计（模型中所有变量为随机变量）下，提出了非参数计量经济联立模型的局部线性两阶段最小二乘估计并利用概率论中大数定理和中心极限定理在内点处研究了它的大样本性质，证明了它的一致性和渐近正态性，它在内点处的收敛速度达到了非参数函数估计的最优收敛速度。     

非参数计量经济联立模型的局部线性两阶段最小二乘变窗宽估计

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用 .本文在随机设计 (模型中所有变量为随机变量 )下 ,提出了非参数计量经济联立模型的局部线性两阶段最小二乘变窗宽估计并利用概率论中大数定理和中心极限定理在内点处研究了它的大样本性质 ,证明了它的一致性和渐近正态性 .它在内点处的收敛速度达到了非参数函数估计的最优收敛速度 .