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柳长青 《数学的实践与认识》2014,(7)
在模型的协变量含有测量误差的情况下,考虑一类泊松回归模型的统计推断问题.通过巧妙地构造辅助随机向量,提出一个工具变量类型的经验似然统计推断方法.证明构造的经验对数似然比函数渐近服从标准卡方分布,进而给出了回归系数的置信区间.所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且具有较好的有限样本性质. 相似文献
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本文考虑部分线性模型的有效经验似然统计推断问题.通过结合模态回归和正交投影技术,提出了一种模态经验似然统计推断过程.证明了提出的经验似然比函数渐近服从中心卡方分布,进而构造了模型参数的置信区间.所提出的估计方法可以对模型的参数分量和非参数分量分别估计,而互不影响,具有较好的稳健性和有效性. 相似文献
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考虑在含有量测噪声情况下的二阶多个体系统聚集控制问题.目的是使得系统中每个个体根据邻居信息构造控制,在只有部分个体能够观测到目标的情况下到达目标.和以前许多多个体同步及聚集问题的研究模型中所考虑的一阶系统不同, 系统的每个个体都只能量测到其邻居个体的部分状态信息,如位置, 并且这些量测还带有噪声.根据这些信息设计了基于局部规则的分散控制律,并且证明当量测噪声和状态量测本身相关时,只要系统在任意给定的时间区域段之内能够保持联合连通,就能够实现系统对目标的跟踪和达到目标. 相似文献
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本文研究强混合样本下随机设计情形线性模型的经验似然推断,将分块技术应用到经验似然方法中,证明了线性模型的参数β的对数经验似然比统计量的渐近分布为卡方分布,由此构造了强混合样本下β的经验似然置信区间.在有限样本情况下给出数值模拟结果. 相似文献
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本文研究强混合样本下部分线性模型的经验似然推断,将分块技术应用到经验似然方法中,证明部分线性模型的参数β的对数经验似然比统计量的渐近分布为卡方分布,由此构造强混合样本下β的经验似然置信区间.在有限样本情况下给出数值模拟结果. 相似文献
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Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large-size clustered data. In this article, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We use eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies . 相似文献
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考虑纵向数据部分线性模型,针对纵向数据个体内的相关性特点,通过引入估计的作业协方差矩阵,构造了模型中未知参数的三种经验对数似然比统计量.在适当条件下,证明了所提出的统计量依分布收敛于χ~2分布,所得结果可以构造未知参数的置信域.最后通过模拟研究对所提方法进行了说明. 相似文献
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In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set. 相似文献
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This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter c... 相似文献
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Yichuan Zhao 《Statistics & probability letters》2011,81(5):603-610
Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method. 相似文献
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The empirical likelihood method is especially useful for constructing confidence intervals or regions of parameters of interest. Yet, the technique cannot be directly applied to partially linear single-index models for longitudinal data due to the within-subject correlation. In this paper, a bias-corrected block empirical likelihood (BCBEL) method is suggested to study the models by accounting for the within-subject correlation. BCBEL shares some desired features: unlike any normal approximation based method for confidence region, the estimation of parameters with the iterative algorithm is avoided and a consistent estimator of the asymptotic covariance matrix is not needed. Because of bias correction, the BCBEL ratio is asymptotically chi-squared, and hence it can be directly used to construct confidence regions of the parameters without any extra Monte Carlo approximation that is needed when bias correction is not applied. The proposed method can naturally be applied to deal with pure single-index models and partially linear models for longitudinal data. Some simulation studies are carried out and an example in epidemiology is given for illustration. 相似文献
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This paper is concerned with feature screening for ultrahigh-dimensional covariates under general varying-coefficient models. With the sparsity principle and based on the conditional distance correlation, we develop a new marginal feature screening procedure called CDC-SIS to select significant covariates and show that it possesses the sure screening property and ranking consistency property under some regularity conditions. The proposed procedure enjoys two appealing merits. First, the model we considered is more flexible than traditional varying-coefficients regression models, so the method can be used in a wider range of applications. Second, CDC-SIS can be used directly to deal with grouped predictor variables and multivariate responses. We assess the finite sample properties of the proposed procedure by Monte Carlo studies, and illustrate our method by an empirical analysis of a real data set. Compared with other similar works, our procedure yields better performance. 相似文献
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A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be equivalent to the mutual information between two distributions of points from the same system separated by infinite time. Thus intuitively, estimation of the bias is reduced to estimation of the mutual information between distributions of data points separated by large time intervals. The proposed bias estimation techniques are shown to work for Lorenz equations data and glucose time series data of three patients from the Columbia University Medical Center database. 相似文献