误差分布未知下时空模型的自适应非参数估计

极大似然估计作为参数估计中较为有效的一种估计方法,在误差分布未知下无法进行,另一方面,时空数据经常含有奇异点或来自重尾分布,此时基于最小二乘的估计方法效果欠佳.考虑时空异质性和相关性,针对误差分布未知的时空模型,本文提出基于核密度估计的自适应非参数估计方法.在较弱的条件下证明了该估计量和已知误差分布下的局部极大似然估计...     

一个有效估计:半参数非时齐扩散模型的局部线性复合分位回归估计

主要研究半参数非时齐扩散模型的参数估计问题.基于非时齐扩散模型的离散观测样本,首先得到漂移参数的局部线性复合分位回归估计,并证明估计量的渐近偏差、渐近方差和渐近正态性.其次,讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,所得到的局部估计较局部线性最小二乘估计更为有效.最后,通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好.     

基于众数回归的部分函数型线性可加模型的稳健估计

本文讨论部分函数型线性可加模型参数的稳健估计,该模型由经典的可加回归模型和函数型线性模型组合而成.采用B-样条基函数对模型中斜率函数和非参数可加函数进行近似,然后通过最大化众数回归目标函数得到基于众数回归的估计.在一些正则条件下,本文给出估计的收敛速度和渐近分布.最后通过模拟计算和应用实例以表明所提方法的有效性.模拟结果表明,该方法不仅具有稳健性,即不易受污染数据或厚尾分布的影响,而且在信噪比较大时可以与最小二乘方法有相同的表现.     

纵向数据半参数回归模型的估计方法

本文考虑纵向数据半参数回归模型,通过考虑纵向数据的协方差结构,基于Profile最小二乘法和局部线性拟合的方法建立了模型中参数分量、回归函数和误差方差的估计量,来提高估计的有效性,在适当条件下给出了这些估计量的相合性.并通过模拟研究将该方法与最小二乘局部线性拟合估计方法进行了比较,表明了Profile最小二乘局部线性拟合方法在有限样本情况下具有良好的性质.     

因变量缺失下部分线性可加模型的估计和检验

本文研究部分线性可加模型在因变量存在缺失情形下的统计推断问题. 首先基于完整数据方法提出了参数分量的Profile 最小二乘估计并证明估计量的渐近正态性. 为了给出参数分量的区间估计,构造了渐近分布为卡方分布的经验似然统计量. 为了检验参数分量的线性约束条件, 构造了调整的广义似然比检验统计量, 当原假设成立时其渐近分布为卡方分布,从而将广义似然比检验推广到了缺失数据情形. 最后通过数值模拟验证所提方法的有效性.     

纵向数据下线性模型的模态回归估计

本文考虑纵向数据下线性回归模型的稳健估计问题.通过结合模态回归(modal regression)方法和二次推断函数(quadratic inference functions)技术,提出了一种基于模态回归的估计过程.证明了回归系数的估计是相合的,并给出了其渐近分布.数据模拟结果表明所提出的估计方法具有较好的稳健性和有效性.     

因变量缺失下部分线性可加模型的估计和检验（英文）

本文研究部分线性可加模型在因变量存在缺失情形下的统计推断问题.首先基于完整数据方法提出了参数分量的Profile最小二乘估计并证明估计量的渐近正态性.为了给出参数分量的区间估计,构造了渐近分布为卡方分布的经验似然统计量.为了检验参数分量的线性约束条件,构造了调整的广义似然比检验统计量,当原假设成立时其渐近分布为卡方分布,从而将广义似然比检验推广到了缺失数据情形.最后通过数值模拟验证所提方法的有效性.     

基于众数回归的变系数部分非线性模型的稳健估计

针对变系数部分非线性模型,提出了一种稳健的基于众数回归的两阶段估计方法.首先,基于B-样条函数近似系数函数,利用QR正交分解技术构造了非线性模型,得到了参数的非线性最小二乘估计.其次,提出了变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

删失数据下的变系数回归模型

研究了删失数据下的变系数回归模型．通过数据变换,利用局部多项式方法,给出了系数函数的局部加权最小二乘估计．证明了该估计的渐近偏差和渐近方差,同时获得了该估计的渐近正态性．     

因变量缺失下线性变量含误差模型的估计

主要考虑线性模型在自变量测量含误差以及因变量缺失情况下的估计问题.对于模型中的回归系数,我们基于最小二乘方法提出了两类估计,其中一类估计只由完整观测数据构成,而另外一类估计利用的则是利用简单插补方法构造的完整数据.证明了这两类估计是渐近正态性的.     

Robust algorithms for multiphase regression models

This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach.     

平行数据模型中异方差问题的处理——截面内误差项U_(it)～ARCH(q)

本文在平行数据模型方差成分的框架下,考虑了横截面内误差项Uit～ARCH(q)的异方差处理方法.给出模型设定的假设检验和参数的一致估计,并利用Monte-Carlo方法验证了本文估计方法优于普通最小二乘估计方法.     

平行数据模型中异方差问题的处理——截面内误差项v_(it)～ARCH(q)

本文在平行数据模型方差成分的框架下,考虑了横截面内误差项v_(it)～ARCH(q)的异方差处理方法。给出模型设定的假设检验和参数的一致估计,并利用Monte-Carlo方法验证了本文估计方法优于普通最小二乘估计方法。     

Robust estimation for varying index coefficient models

Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. doi: 10.1080/01621459.2014.903185) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation–maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.     

Outlier detection and robust covariance estimation using mathematical programming

The outlier detection problem and the robust covariance estimation problem are often interchangeable. Without outliers, the classical method of maximum likelihood estimation (MLE) can be used to estimate parameters of a known distribution from observational data. When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them. Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions. However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance. An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given smaller weights and can be detected. This method produces a covariance estimator that has the following properties: First, it is affine equivariant. Second, it is computationally efficient even for large problem sizes. Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method is tested for different contamination models, including recently proposed ones. The method is not only faster than the Fast-MCD method for high dimensional data but also has reasonable accuracy for the tested cases.     

Modal Regression Based on Nonparametric Quantile Estimator

Modal regression based on nonparametric quantile estimator is given. Unlike the traditional mean and median regression, modal regression uses mode but not mean or median to represent the center of a conditional distribution, which helps the model to be more robust for outliers, asymmetric or heavy-taileddistribution. Most of solutions for modal regression are based on kernel estimation of density. This paper studies a new solution for modal regression by means of nonparametric quantile estimator. This method builds on the fact that the distribution function is the inverse of the quantile function, then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function. The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation.     

Permutation tests using least distance estimator in the multivariate regression model

This paper proposes two permutation tests based on the least distance estimator in a multivariate regression model. One is a type of t test statistic using the bootstrap method, and the other is a type of F test statistic using the sum of distances between observed and predicted values under the full and reduced models. We conducted a simulation study to compare the power of the proposed permutation tests with that of the parametric tests based on the least squares estimator for three types of hypotheses in several error distributions. The results indicate that the power of the proposed permutation tests is greater than that of the parametric tests when the error distribution is skewed like the Wishart distribution, has a heavy tail like the Cauchy distribution, or has outliers.     

生长曲线模型的分位数回归

生长曲线模型有着广泛的应用, 在经济学、生物学、医学等各个领域的研究都起着重要的作用. 已有文献关于生长曲线模型参数矩阵的估计基本上是使用最小二乘方法或极大似然方法. 使用最小二乘方法, 当误差项服从偏峰分布、厚尾分布、或者存在异常点时, 得出的估计不是有效的; 使用极大似然方法, 要求分布已知, 实际使用时很难满足这一点. 分位数回归能弥补如上这些缺陷, 所得估计具有很好的稳健性. 本文使用分位数回归方法给出生长曲线模型参数矩阵的估计, 及其渐近正态性.     

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In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

基于汇率回报厚尾性的外汇期权定价模型

主要研究汇率回报呈厚尾分布的外汇期权定价问题。本文利用t-分布能捕获汇率回报序列厚尾特征的优势，推导出基于t-分布外汇期权定价模型的解析表达式，即对外汇期权定价模型——BSGK模型进行了修正，同时应用矩估计法估计出的t-分布的自由度用于该定价模型的计算，最后基于t-分布的外汇期权定价模型和BSGK外汇期权定价模型进行了比较分析。