统计学-部分经典文献

Estimation in Two Classes of Semiparametric Diffusion Models两类半参数扩散模型的估计In this paper we propose an estimation method for two classes of semiparametric scalar diffusion models driven by a Brownian motion: In the first class, only the diffusion term is parameterised while the drift is unspecified; in the second, the drift term is specifified while the diffffusion is of unknown form. The estimation method is based on the assumption of stationarity of the observed process. This allows us to express the unspecified term as a functional of the parameteric part and the stationary density. A MLE-like estimator for the parametric part and a kernel estimator of the nonparametric part are defined for a discrete sample with a fixed time distance between the observations. We show that the parametric part of the estimator is n consistent while the nonparametric part has a slower convergence rate. Also, the asymptotic distribution of the estimator is derived. To illustrate the usefulness of these two classes, we fit a specific model from the first class to a proxy of the Eurodollar short-term interest rate. We find non-linearities in both the drift and diffusion function that standard parametric models are unable to capture.本文提出了两类半参数标量的估计方法由布朗运动驱动的扩散模型：在第一类中，只有扩散项参数化，而漂移是未指定的；在第二种情况下，漂移项被指定，而扩散项形式未知。

估计方法是基于的假设观测过程的平稳性。

这允许我们将未指定项表示为参数部分的函数和稳态密度。

对于有固定观测时间距离的离散样本，定义了参数部分的极大似然估计量和非参数部分的核估计量。

我们证明了参数部分估计量是n一致的，而非参数部分收敛速度较慢。

同时，给出了估计量的渐近分布。

为了说明这两个类的有用性，我们将第一个类拟合一个特定模型与欧洲美元短期利率的代表相匹配。

我们发现，漂移和扩散函数的非线性标准参数模型无法捕获。

Statistical estimation in variable coefficient models变系数模型的统计估计Varying coefficient models are a useful extension of classical linear models. They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age. The appeal of these models is that the coefficient functions can easily be estimated via a simple local regression. This yields a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when different coefficient functions admit different degrees of smoothness. This drawback can be repaired by using our proposed two-step estimation procedure. The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an application to an environmental data set.变系数模型是经典线性模型的一个有用的推广模型。

当一个人想要研究回归系数在不同的群体中是如何变化的，并以特定的协变量(如年龄)为特征时，回归系数就会自然地出现。

这些模型的优点是通过简单的局部回归就可以很容易地估计出系数函数。

这产生了一个简单的一步估计过程。

我们证明，当不同的系数函数有不同的平滑度时，这种一步法不可能是最优的。

这个缺陷可以通过使用我们提出的两步估计过程来修复，得到了两步法的渐近均方误差，并证明了其收敛速度是最优的。

一些仿真研究表明，两步法实现的程序可能相当复杂。

该方法通过应用于环境数据集进行了说明。

Analysis of Longitudinal Data With Semiparametric Estimation ofCovariance Function半参数纵向数据分析协方差函数的估计Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed.A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure－a quasi-likelihood approach and a minimum generalized variance method－are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies.The proposed methodology is illustrated with an analysis of a real data example.提高/改进回归系数的效率和预测个体轨迹是纵向数据分析的两个重要方面。

两者都涉及到协方差函数的估计。

然而，在估计不规则时间点收集的纵向数据协方差函数时出现了挑战。

提出了一类协方差函数的半参数模型，该模型在允许通过强加一个参数关联结构到非参数方差函数。

提出了一种估计非参数方差函数的核估计量。

关联结构中参数的估计有两种方法，拟似然法和最小广义方差法。

介绍了一种纵向数据半参变系数部分线性模型，及一种基于剖面加权最小二乘法的模型系数估计方法。

研究了估计过程的抽样性质，建立了估计量的渐近正态性。

通过蒙特卡罗模拟对所提方法的有限样本性能进行了评估，并以一个实际数据案例分析，对提出的方法予以说明。