m（n）－相依样本非参数回归残差密度的相合估计

考虑非参数回归模型：Ｙ_i＝Ｍ（Ｘ_i）＋ｅ_i，其中Ｍ（ｘ）为Ｂ（?Ｒ）上的未知实函数，（Ｘ_i，Ｙ_i）为来自（Ｘ，Ｙ）的ｍ（ｎ）相依样本，残差（ｅ_i）具有公共的未知密度ｆ（ｘ）．本文基于残差估计给出了ｆ（ｘ）的一种非参估计，并证明该估计具有逐点相合性，一致相合性及Ｌ₁相合性．     

删失数据回归误差项的非参数密度估计的一致相合性(英文)

回归误差项是不可观测的. 由于回归误差项的密度函数在实际中有许多应用, 故使用非参数方法对其进行估计就成为回归分析中的一个基本问题. 针对完全观测数据回归模型, 曾有作者对此问题进行了研究. 然而在实际应用中, 经常会有数据被删失的情况发生, 在此情况下, 可以利用删失回归残差, 并使用核估计的方法对回归误差项的密度函数进行估计. 本文研究了该估计的大样本性质, 并证明了估计量的一致相合性.     

TLS问题和LS问题解加权残量的比较

总体最小二乘(TLS)问题和最小二乘(LS)问题解残量的比较已有多篇文献予以探讨.本文对TLS问题和LS问题解的加权残量进行了比较. 导出了TLS解、改进的LS解及普通LS解加权残量之间的误差界. 从而进一步完善了已有的相关结果.     

Production mechanism of neutron-rich nuclei around N =126 in the multi-nucleon transfer reaction ~(132)Sn+~(208)Pb

The time-dependent Hartree-Fock approach in three dimensions is employed to study the multi-nucleon transfer reaction~(132) Sn +~(208) Pb at various incident energies above the Coulomb barrier. Probabilities for different transfer channels are calculated by using the particle-number projection method. The results indicate that neutron stripping(transfer from the projectile to the target) and proton pick-up(transfer from the target to the projectile)are favored. De-excitation of the primary fragments is treated by using the state-of-art statistical code GEMINI++.Primary and final production cross sections of the target-like fragments(with Z =77 to Z =87) are investigated. The results reveal that fission decay of heavy nuclei plays an important role in the de-excitation process of nuclei with Z 82. It is also found that the final production cross sections of neutron-rich nuclei depend only slightly on the incident energy, while those of neutron-deficient nuclei depend strongly on the incident energy.     

A Weighted Goodness-of-Fit Test for GARCH(1,1) Specification

Suppose that (j) is the lag-j autocorrelation of the squared residuals computed from a realization of length n under the assumption that the observations follow a GARCH(1,1) model. We study the asymptotic distribution of the statistics of the form , where the _j are nonnegative summable weights and the matrix , can be estimated from the data. We show that, under weak assumptions on model errors, the statistic Q _n converges in distribution to , where the N _i are iid standard normal. We discuss choices of the weights _j for which the distribution of Q is tabulated. Our results lead to and provide a rigorous justification for Portmanteau goodness-of-fit tests for GARCH(1,1) specification.     

Diagnostic analysis of experimental artefacts in DOSY NMR data by covariance matrix of the residuals

Multivariate curve resolution (MCR) has been applied to separate pure spectra and pure decay profiles of DOSY NMR data. Given good initial guesses of the pure decay profiles, and combined with the nonlinear least square regression (NLR), MCR can result in good separation of the pure components. Nevertheless, due to the presence of artefacts in experimental data, validation of a MCR model is still necessary. In this paper, the covariance matrix of the residuals (CMR), obtained by postmultiplying the residual matrix with its transpose, is proposed to evaluate the quality of the results of an experimental data set. Plots of the rows of this matrix give a general impression of the covariance in the frequency domain of the residual matrix. Different patterns in the plot indicate possible causes of experimental imperfections. This new criterion can be used as diagnosis in order to improve experimental settings as well as suggest appropriate preprocessing of DOSY NMR data.     

The hat matrix for smoothing splines

The matrix which transforms the data vector to the vector of fitted values for smoothing splines is termed the hat matrix. This matrix is shown to have many of the same properties, and is seen to play the same role in the variances and covariances of the residuals, as its regression analysis counterpart. This fact is utilized to propose several possible diagnostic measures for use with smoothing splines. The extension of these results to include multivariate Laplacian smoothing spline is also indicated.     

强非线性自激振动问题的瞬态解

用新的改进的L-P法并结合权残法求得了一般情况下(阻尼项可以不是小量)强非线性自激振动问题的一级近似瞬态解。近似解有很好的精度。     

基于半参数回归模型的残差控制图

本文探讨产品工作状态(而非工作结果)的监控,即产品质量特性值随时间和其他影响因素变化的工作过程的监控。受到卷烟生产中叶丝干燥出口物料含水率的监控问题的启发,本文提出了基于半参数回归模型的残差控制图,即通过拟合半参数回归模型获得残差,将经过标准化变换、去自相关性处理和正态变换后的残差作为描点统计量作于Shewhart控制图中,从而进行产品过程工作状态的质量监控。实例分析显示,本文方法对过程均值的异常反应灵敏,能有效地应用于实际生产中。     

ASYMPTOTICS OF THE RESIDUALS DENSITY ESTIMATION IN NONPARAMETRIC REGRESSION UNDER m（n）-DEPENDENT SAMPLE

Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.