讨论具有不同自变量的变系数模型的函数系数的估计及其大样本性质使用局部线性方法和积分方法，得到函数系数的积分估计由于该估计有较大的方差，进一步使用回切法改进这一估计，获得了函数系数的改进估计同时，研究了改进估计的渐近正态性最后，用模拟例子说明提出的估计方法是有效的。

半变系数模型已经获得了广泛的研究和应用，近几年，人们提出许多方法来估计其函数系数和常系数。在PLS方法基础上，本文给出半变系数模型模型在线性随机约束条件下的估计，并证明了常系数和函数系数估计的渐近正态性。

In this paper, we are concerned with statistical inference for the index parameter α0 in the single-index model Y=g (αT0X) + ε. Based on the estimates obtained by the local linear method, we extend the generalized likelihood ratio test to the single-index model. We investigate the asymptotic behaviour of the proposed test and demonstrate that its limiting null distribution follows a 2-distribution, with the scale constant and the number of degrees of freedom being independent of nuisance parameters or functions, which is called the Wilks phenomenon. A simulated example is used to illustrate the performance of the testing approach.

To perform hydrological forecasting, time series methods are often employed. In univariate time series, the autoregressive integrated moving average (ARIMA) model, the seasonal autoregressive moving average (SARMA) model, the deseasonalized model and the periodic autoregressive (PAR) model are often used. These models are based on the assumption that the influence of lagged riverflows on the riverflow is linear. In reality the assumption is often questionable. In this paper, the functional-coefficient autoregression (FCAR) model, which is a nonlinear model, is introduced to forecast riverflows. To explore the influence of the inflow on the outflow in a river system and to exploit the internal interaction of the outflows, bivariate time series models are needed. The transfer function (TF) model and the semi-parametric regression (SPR) model are often employed. In this paper, a new model, the non-parametric and functional-coefficient autoregression (NFCAR) model, is proposed. It consists of two parts: the first part, the non-parametric part explains the influences of the inflows on the outflow in a river system; the second part, the functional-coefficient linear part reveals the interactions among the outflows in a river system. By comparing the calibration and forecasting of the models, it is found that the NFCAR model performs very well.

This paper considers statistical inference for semiparametric varying coefficient partially linear models with error-prone linear covariates. An empirical likelihood based statistic for parametric component is developed to construct confidence regions. The resulting statistic is shown to be asymptotically chi-square distributed. By the empirical likelihood ratio function, the maximum empirical likelihood estimator of the parameter is defined and the asymptotic normality is shown. A simulation experiment is conducted to compare the empirical likelihood, normal based and the naive empirical likelihood methods in terms of coverage accuracies of confidence regions.