A Recursive Algorithm to Restore Images Based on Robust Estimation of NSHP Autoregressive Models

The objective of this article is to present a new image restoration algorithm. First, each pixel in the image is classified into k categories. Then we assume that the gray levels in each category follow a nonsymmetric half-plane (NSHP) autoregressive model. Robust estimation of the parameters of the model is considered to attenuate the effect of the image contamination on the parameters. In each iteration we will construct a new image using a robustified version of the residuals. The introduction of the classification techniques as a first step of the algorithm reduces considerably the number of parameters to estimate. Hence, the computational time is also reduced because the robust estimations of the parameters are solutions of nonlinear system of equations. Some applications are presented to real synthetic aperture radar (SAR) images to illustrate how our algorithm restores an image in practice.     

Estimating the Innovation Distribution in Nonlinear Autoregressive Models

The usual estimator for the expectation of a function under the innovation distribution of a nonlinear autoregressive model is the empirical estimator based on estimated innovations. It can be improved by exploiting that the innovation distribution has mean zero. We show that the resulting estimator is efficient if the innovations are estimated with an efficient estimator for the autoregression parameter. Efficiency of this estimator is necessary except when the expectation of the function can be estimated adaptively. Analogous results hold for heteroscedastic models.     

Wavelet-Based Detection of Outliers in Time Series

This article considers the problem of detecting outliers in time series data and proposes a general detection method based on wavelets. Unlike other detection procedures found in the literature, our method does not require that a model be specified for the data. Also, use of our method is not restricted to data generated from ARIMA processes. The effectiveness of the proposed method is compared with existing outlier detection procedures. Comparisons based on various models, sample sizes, and parameter values illustrate the effectiveness of the proposed method.     

General Autoregressive Models with Long-Memory Noise

We give the limiting distribution of the least-squares estimator in the general autoregressive model driven by a long-memory process. We prove that with an appropriate normalization the estimation error converges, in distribution, to a random vector which contains: (1) a stochastic component, due to the presence of the unstable roots, which are multiple Wiener–Itô integrals and a non-linear functionals of stochastic integrals with respect to a Brownian motion; (2) a constant component due to the stable roots; (3) a stochastic component, due to the presence of the explosive roots, which is a mixture of normal distributions.     

Data Clustering Based on Maximization of Outlier Factor

There exist many data clustering algorithms, but they can not adequately handle the number of clusters or cluster shapes. Their performance mainly depends on a choice of algorithm parameters. Our approach to data clustering and algorithm does not require the parameter choice; it can be treated as a natural adaptation to the existing structure of distances between data points. The outlier factor introduced by the author specifies a degree of being an outlier for each data point. The outlier factor notion is based on the difference between the frequency distribution of interpoint distances in a given dataset and the corresponding distribution of uniformly distributed points. Then data clusters can be determined by maximizing the outlier factor function. The data points in dataset are divided into clusters according to the attractor regions of local optima. An experimental evaluation of the proposed algorithm shows that the proposed method can identify complex cluster shapes. Key advantages of the approach are: good clustering properties for datasets with comparatively large amount of noise (an additional data points), and an absence of important parameters which adequate choice determines the quality of results.     

Robust Estimation for Generalized Additive Models

This article studies M-type estimators for fitting robust generalized additive models in the presence of anomalous data. A new theoretical construct is developed to connect the costly M-type estimation with least-squares type calculations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall M-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis. Supplementary materials are available online.     

异常交易行为的甄别研究

本文在无指导学习的研究框架下,运用分位数回归模型结合变点检验,对中国证券市场的异常交易行为进行甄别研究。通过分析持股比例变动与股价收益率间协同演化关系的异常,为甄别异常交易行为设立判别标准并客观的界定阈值提供了一种新的方法。基于这一方法监管者可以构建分期、分级、分类的实时监管体系,提高监管效率。     

Testing Changes in Hilbert Space Autoregressive Models

We consider a polygonal line process based on residual partial sums of a stationary Hilbert space-valued autoregressive process. Its convergence to a Hilbert space-valued Brownian motion is established in the framework of Hölder spaces. The relevance of the results to the problem of testing stability of {ARH}$(1)$ model under different types of alternatives is discussed.     

删失回归模型中的变量选择

在一个删失回归模型("Tobit"模型)中,我们常常要研究如何选择重要的预报变量.本文提出了基于信息理论准则的两种变量选择程序,并建立了它们的相合性.     

函数系数线性自回归模型的样条估计

基于多项式样条全局光滑方法,建立函数系数线性自回归模型中系数函数的样条估计.在适当条件下,证明了系数函数多项式样条估计的相合性,并给出了它们的收敛速度.模拟例子验证了理论结果的正确性.     

广义自回归模型参数的收缩估计

运用经典方法结合参数的先验信息得到了广义一阶自回归模型中自相关系数的收缩估计的闭式表达式,它是通常极大似然估计与先验均值的加权平均,在适当的先验信息下优于原来的估计.     

基于协变量缺失的Horvitz-Thompson加权分位回归估计方法

含有协变量缺失的数据缺失问题是现代统计分析中的热点之一.当缺失数据中同时存在厚尾,偏斜和异方差问题时则更加难以处理.为此,本文提出一种逆概率加权分位回归估计来研究响应和协变量之间的关系.与经典估计方法相比具有明显优势,一方面,该估计量使用了所有可用的数据,并且允许缺失的协变量与响应高度相关;另一方面,该估计量在所有分位数水平上满足一致性和渐近正态性.通过模拟验证了该方法的在有限样本下的有效性,进一步将该方法推广到线性多元回归模型和非参数回归模型.     

基于局部多项式展开的多元非参数模型贝叶斯带宽选择

在多元非参数模型中带宽和阶的选择对局部多项式估计量的表现十分重要。本文基于交叉验证准则提出一个自适应贝叶斯带宽选择方法。在给定的误差密度函数下,该方法可推导出对应的似然函数,并构造带宽参数的后验密度函数。随后,通过带宽的后验期望可同时获得阶和带宽的估计。数值模拟的结果表明,该方法不仅比大拇指准则方法精确,且比交叉验证方法耗时更少。与此同时,与Nadaraya-Watson估计相比,所提带宽选择方法对多元非参数模型的适应性要更好。最后,本文通过一组实际数据说明有限样本下所提贝叶斯带宽选择的表现很好。     

OUTLIER TEST IN RANDOMIZED LINEAR MODEL

In this paper, we give an approach for detecting one or more outliers inrandomized linear model The likelihood ratio test statistic and its distributions under the null hypothesis and the alternative bypothesis are given. Furthermore, the rebustneas of the test statistic in a certain sere is proved. Finally, the optimality properties of the test are derived.     

基于非参数密度估计的异常点诊断方法

异常点诊断是统计学中的经典问题.发现并减少异常点对纳税评估数据分析的影响是一项很有意义的研究.然而,通常的异常点诊断一般采用适用于单峰分布的全局识别方法.借鉴局部域相关积分(Local correlation integral)理论,提出基于非参数密度估计的识别方法.方法适用于多峰分布,能识别局域性质的异常点,对异常点占比较高的样本也有较强的识别能力.基于某市10 920个企业样本,实证分析对比研究了税务局目前使用的和建议的纳税评估方法,结果表明税务局采用的方法有较大的纳税评估风险(误判风险).     

Estimating the Density of the Residuals in Autoregressive Models

We consider a (nonlinear) autoregressive model with unknown parameters (vector θ). The aim is to estimate the density of the residuals by a kernel estimator. Since the residuals are not observed, the usual procedure for estimating the density of the residuals is the following: first, compute an estimator for θ; second, calculate the residuals by use of the estimated model; and third, calculate the kernel density estimator by use of these residuals. We show that the resulting density estimator is strong consistent at the best possible convergence rate. Moreover, we prove asymptotic normality of the estimator. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于极值理论的EXPAR时序模型异常点诊断

本文基于极值理论给出诊断EXPAR模型异常点检验统计量的渐近分布,并依此渐近分布来选取检验的临界值。这种方法选取的临界值可保证控制在一定显著性水平下,而且可以计算渐近p值,比仿真选取的临界值更科学合理。     

基于贝叶斯法则的空间自相关误差自相关模型变量选择研究

本文将研究贝叶斯法则视角下的空间自相关误差自相关模型(Spatial Autoregressive Model with Autoregressive Disturbances,SARAR模型)变量选择问题。通过将基于BIC准则的子集选择法推广到空间模型,实现SARAR模型的变量选择,并证明在一定条件下,对于SARAR模型的变量选择BIC准则具有良好的渐近性质。同时本文还将利用Monte Carlo模拟验证BIC准则能够很好的实现SARAR模型的变量选择。最后以股票收益率为例,在验证股票收益率具有空间效应的前提下,利用BIC准则对影响股票收益率的众多财务指标进行变量选择。     

Variational Approximation for Mixtures of Linear Mixed Models

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the Expectation–Maximization algorithm. A suitable number of components is then determined conventionally by comparing different mixture models using penalized log-likelihood criteria such as Bayesian information criterion. We propose fitting MLMMs with variational methods, which can perform parameter estimation and model selection simultaneously. We describe a variational approximation for MLMMs where the variational lower bound is in closed form, allowing for fast evaluation and develop a novel variational greedy algorithm for model selection and learning of the mixture components. This approach handles algorithm initialization and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparameterize the model and show empirically that there is a gain in efficiency in variational algorithms similar to that in Markov chain Monte Carlo (MCMC) algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler, which suggests that reparameterizations can lead to improved convergence in variational algorithms just as in MCMC algorithms. Supplementary materials for the article are available online.     

Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners

The complexity of linear mixed-effects (LME) models means that traditional diagnostics are rendered less effective. This is due to a breakdown of asymptotic results, boundary issues, and visible patterns in residual plots that are introduced by the model fitting process. Some of these issues are well known and adjustments have been proposed. Working with LME models typically requires that the analyst keeps track of all the special circumstances that may arise. In this article, we illustrate a simpler but generally applicable approach to diagnosing LME models. We explain how to use new visual inference methods for these purposes. The approach provides a unified framework for diagnosing LME fits and for model selection. We illustrate the use of this approach on several commonly available datasets. A large-scale Amazon Turk study was used to validate the methods. R code is provided for the analyses. Supplementary materials for this article are available online.