An Efficient Multiple Imputation Approach for Estimating Equations with Response Missing at Random and High-Dimensional Covariates

Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.     

Two-step estimators in partial linear models with missing response variables and error-prone covariates

A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.     

含屏蔽数据四单元混联系统的可靠性分析

讨论了两种含屏蔽数据四单元混联系统的可靠性分析问题。在单元失效率为指数函数的情形下,详细推导出两种混联系统在逐步Ⅱ型混合截尾试验下的似然函数。利用极大似然方法给出了单元分布参数及系统可靠度函数的极大似然估计,采用似然比方法构造了未知参数的近似置信区间。最后运用蒙特卡罗方法进行随机模拟,验证了所提方法的正确性和有效性。     

截断非平衡似无关模型的极大仿真似然估计

样本数据缺失和截断是现代统计调查中经常遇到的两个问题，它们在一定程度上影响模型参数估计的准确性和有效性. 该研究首先提出了一个新的截断非平衡似无关回归模型，这个模型能够同时考虑数据缺失和截断的特征；然后基于Geweke-Hajivassiliou-Keane（GHK）的仿真算子，建立了该模型的极大仿真似然估计方法；蒙特卡罗实验结果表明，在大样本和有限样本下这种估计方法在参数估计的准确性和有效性方面均具有良好表现.     

Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems

In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.     

Adjusted Empirical Likelihood Estimation of Distribution Function and Quantile with Nonignorable Missing Data

This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the Horvtiz-Thompson-type method, regression imputation method and augmented inverse probability weighted approach. The propensity score is specified by a semiparametric exponential tilting model. To estimate the tilting parameter in the propensity score, the authors propose an adjusted empirical likelihood method to deal with the over-identified system. Under some regular conditions, the authors investigate the asymptotic properties of the proposed three estimators for distribution functions and quantiles, and find that these estimators have the same asymptotic variance. The jackknife method is employed to consistently estimate the asymptotic variances. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies.     

相似产品步进应力加速寿命试验的统计分析

本文将单组样本的步进应力加速寿命试验(SSALT)拓展到双样本情形.基于累积失效模型(CEM),对两组指数产品的联合Ⅱ型截尾数据进行综合分析.首先,计算未知参数的极大似然估计(MLE),并利用矩母函数(MGF)建立其条件概率分布.然后,采用两种方法,基于概率分布的精确分析方法和参数的Bootstrap方法,构建参数的置信区间(CIs).以覆盖率作为评价标准,对两种方法的区间估计效果进行分析.最后,通过数值算例验证了本文方法的有效性.     

Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-Ⅰ Hybrid Censoring

This paper investigates a simple step-stress accelerated lifetime test(SSALT) model for the inferential analysis of exponential competing risks data. A generalized type-I hybrid censoring scheme is employed to improve the efficiency and controllability of the test. Firstly, the MLEs for parameters are established based on the cumulative exposure model(CEM). Then the conditional moment generating function(MGF) for unknown parameters is set up using conditional expectation and multiple integral techniques. Thirdly, confidence intervals(CIs) are constructed by the exact MGF-based method, the approximate normality-based method, and the bias-corrected and accelerated(BCa) percentile bootstrap method. Finally, we present simulation studies and an illustrative example to compare the performances of different methods.     

Sieve least squares estimator for partial linear models with current status data

Current status data often arise in survival analysis and reliability studies, when a continuous response is reduced to an indicator of whether the response is greater or less than an observed random threshold value. This article considers a partial linear model with current status data. A sieve least squares estimator is proposed to estimate both the regression parameters and the nonparametric function. This paper shows, under some mild condition, that the estimators are strong consistent. Moreover, the parameter estimators are normally distributed, while the nonparametric component achieves the optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed estimates. For illustration purposes, the method is applied to a real dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.     

Parsimonious Mean-Covariance Modeling for Longitudinal Data with ARMA Errors

Based on the generalized estimating equation approach, the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process, which not only unites the existing autoregressive Cholesky factor model and moving average Cholesky factor model but also provides a wide variety of structures of covariance matrix. The resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild conditions. The authors demonstrate the effectiveness, parsimoniousness and desirable performance of the proposed approach by analyzing the CD4+ cell counts data set and conducting extensive simulations.     

数据丢包的参数不确定下无人机滚动时域估计

针对网络中通信链路中断及系统参数不确定现象,研究了数据包丢失的参数不确定无人机系统状态估计问题,基于滚动时域估计理论和随机最小二乘理论,提出了一种分布式滚动时域估计算法。对于数据包丢失和参数不确定问题,采用已知概率的马尔可夫序列和系统矩阵扰动噪声进行建模。仿真结果表明,该算法的估计效果优于一种新的卡尔曼滤波算法。最后,研究分析了系统压缩量、数据包接收概率和时窗长度对所提算法估计性能的影响。在系统不确定性和丢包概率未知的情况下,适当增加时窗长度可以提高算法估计性能。     

TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated （SU） non- parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologie study are used to illustrate the proposed procedure.     

Robust estimation of parameters in nonlinear ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to model dynamic processes in many scientific fields. Parameter estimation is usually a challenging problem, especially in nonlinear ODE models. The most popular method, nonlinear least square estimation, is shown to be strongly sensitive to outliers. In this paper, robust estimation of parameters using M-estimators is proposed, and their asymptotic properties are obtained under some regular conditions. The authors also provide a method to adjust Huber parameter automatically according to the observations. Moreover, a method is presented to estimate the initial values of parameters and state variables. The efficiency and robustness are well balanced in Huber estimators, which is demonstrated via numerical simulations and chlorides data analysis.     

一种基于解压的镜头探测方法

镜头探测是视频内容和结构化分析的第一步。目前的镜头探测方法根据处理角度不同 ,主要分为压缩域和解压域两种。提出了一种基于解压的镜头探测方法。该方法基于这样一个假定 ,即同一镜头往往具有相同的背景区域。通过对背景区域的数据进行分析 ,得到视频的镜头边界。该方法具有设置参数少、阈值敏感度低以及处理数据量小的特点 ,适用于大容量的视频库。通过对各种不同类型的视频进行实验 ,证明该方法具有较强的适应性和鲁棒性 ,可以获得较高的镜头查到率和查准率     

自回归模型的加权复合Expectile回归估计及其应用

本文基于充分利用多个Expectile信息能提高参数估计效率的假设,提出了AR模型的加权复合Expectile回归(WCER)估计,探讨了该估计的最优权重,建立了其大样本性质,发现根据由数据驱动的最优权重所获得的WCER估计与最优权重已知时所获得的WCER估计具有相同的渐近有效性.数值模拟表明,当误差为厚尾或非对称分布,所提出的WCER估计大大优于传统最小二乘估计.即使误差分布未知,依然可以得到像极大似然估计一样具有优良统计性质的WCER估计.应用所提出的方法分析恒生指数和标准普尔500指数,实证分析表明:所提出的WCER估计在有效性意义下非常具有竞争力.     

Variable selection in joint location,scale and skewness models of the skew-normal distribution

Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and (or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes, and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.     

Smooth estimation of ROC curve in the presence of auxiliary information

Receiver operating characteristic (ROC) curve is often used to study and compare two-sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error (MSE). Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.     

数论网格法在极大似然估计中的应用

复杂似然函数的多峰性使得极大似然估计的求解存在很大困难。针对这一问题,提出了求解极大似然估计问题的数论网格法。讨论了数论网格法的特点,理论分析了其算法精度,给出了基于数论网格的序贯优化算法的计算步骤,研究了初始搜索区域和算法初始参数的确定方法。最后,以两参数威布尔分布参数极大似然估计为例,给出了极大似然估计的计算过程,比较了序贯优化算法和对分法的估计结果,说明了序贯优化算法的有效性和计算效率。     

不等定时截尾试验指数分布情形下的可靠性评定

针对产品的可靠性评估问题,一般需要统计分析寿命试验中收集到的试验数据。假如所有试验样品都在不同时刻终止试验,这种方式就是不等定时截尾寿命试验。针对不等定时截尾数据,现有方法大多只能得到参数的点估计,缺乏针对参数置信区间的估计方法。针对这一问题,在指数分布下,根据样本空间排序法这一理论,推导得到一个比现有方法更简单的计算方法。作为对比,基于极大似然估计的性质和bootstrap方法,又提出两个置信下限的近似求解方法。然后,通过蒙特卡罗仿真实验和一个算例,比较了这3个方法。实验表明基于样本空间排序法的计算结果更优。     

Feature Screening for Nonparametric and Semiparametric Models with Ultrahigh-Dimensional Covariates

This paper considers the feature screening and variable selection for ultrahigh dimensional covariates. The new feature screening procedure base on conditional expectation which is used to differentiate whether an explanatory variable contributes to a response variable or not, without requiring a specific parametric form of the underlying data model. The authors estimate the marginal conditional expectation by kernel regression estimator. The proposed method is showed to have sure screen property. The authors propose an iterative kernel estimator algorithm to reduce the ultrahigh dimensionality to an appropriate scale. Simulation results and real data analysis demonstrate the proposed method works well and performs better than competing methods.