Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

Testing conditional independence with data missing at random

It is known that conditional independence is a quite basic assumption in many fields of statistics. How to test its validity is of great importance and has been extensively studied by the literature. Nevertheless, all of the existing methods focus on the case that data are fully observed, but none of them seems having taken into account of the scenario when missing data are present. Motivated by this, this paper develops two testing statistics to handle such a situation relying on the idea of inverse probability weighted and augmented inverse probability weighted techniques. The asymptotic distributions of the proposed statistics are also derived under the null hypothesis. The simulation studies indicate that both testing statistics perform well in terms of size and power.

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.

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.

A class of weighted estimating equations for additive hazards models with covariates missing at random

Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.

The abstract of doctoral dissertation‘nonlinear wavelet density estimation and hazard rate estimation with data missing at random’

In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.

CBPS-Based Inference in Nonlinear Regression Models with Missing Data

In this article, to improve the doubly robust estimator, the nonlinear regression models with missing responses are studied. Based on the covariate balancing propensity score (CBPS), estimators for the regression coefficients and the population mean are obtained. It is proved that the proposed estimators are asymptotically normal. In simulation studies, the proposed estimators show improved performance relative to usual augmented inverse probability weighted estimators.

Using Statistical Learning to Treat Missing Data: A Case of HIV/TB Co-Infection in Kenya

In this study, we investigate the effects of missing data when estimating HIV/TB co-infection. We revisit the concept of missing data and examine three available approaches for dealing with missingness. The main objective is to identify the best method for correcting missing data in TB/HIV Co-infection setting. We employ both empirical data analysis and extensive simulation study to examine the effects of missing data, the accuracy, sensitivity, specificity and train and test error for different approaches. The novelty of this work hinges on the use of modern statistical learning algorithm when treating missingness. In the empirical analysis, both HIV data and TB-HIV co-infection data imputations were performed, and the missing values were imputed using different approaches. In the simulation study, sets of 0% (Complete case), 10%, 30%, 50% and 80% of the data were drawn randomly and replaced with missing values. Results show complete cases only had a co-infection rate (95% Confidence Interval band) of 29% (25%, 33%), weighted method 27% (23%, 31%), likelihood-based approach 26% (24%, 28%) and multiple imputation approach 21% (20%, 22%). In conclusion, MI remains the best approach for dealing with missing data and failure to apply it, results to overestimation of HIV/TB co-infection rate by 8%.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

基于FPGA的光通信误码率测试系统设计

误码率是数据传输设备的衡量指标之一,误码率测试是SFP光通信模块生产与设计中重要的环节。针对SFP光通信模块设计了一种基于FPGA的误码率测试系统,系统采用并行m型伪随机序列编码,可实现PRBS-7至PRBS-31标准的m序列码流生成,与SFP光通信模块的通信速率为1.25Gbps。系统打破常规测试的局限性,模块连接简便,可以在短时间内对SFP光通信模块进行准确测试,提高了SFP光通信模块误码率测试的效率。

海量数据下多指标含大量缺失的因果推断

因果推断中,常存在大量的缺失数据,特别是当协变量和结局变量都存在着缺失数据问题,如果处理不好,获得的估计可能会存在着偏误。文章在基于倾向评分逆概加权方法估计处理效应的基础上,调整权重为不只是倾向评分加权,还有协变量的缺失机制和结局变量缺失机制的加权,给出处理效应估计方法。应用delta方法给出估计量的渐近方差,借助模拟研究验证了因果效应估计量及其渐近方差估计的正确性和可行性,并与传统方法做比较,本文得到的估计量的Bias和MSE都较优于传统方法。

针刺与自拟方联合西药治疗糖尿病周围神经病变随机平行对照研究

[目的]观察针刺与自拟方联合西药治疗糖尿病周围神经病变疗效。[方法]使用随机平行对照方法,将76例门诊患者按就诊顺序编号法简单随机分为两组。对照组34例西医常规治疗,口服降糖药、饮食调理、胰岛素注射和合理运动等,将血糖控制在正常范围内后予以神经营养支持,口服维生素B1、维生素B12和地巴唑,药量根据患者病情决定。治疗组42例自拟方(山药10g,熟地黄、茯苓、黄芪各30g,天花粉20g,当归15g,葛根10g,川芎15g,泽泻、丹皮各12g,白芍15g,丹参20g、赤芍15g,木香10g;盗汗、烦热、失眠加黄柏10g,知母12g;畏寒恶冷、四肢欠温加淡附子3g,肉桂6g;肢体明显疼痛加乳香、没药各9g,延胡索炒15g;烦渴的加栀子、知母各2g),水煎200m L,早晚温服;西医常规治疗同对照组。连续治疗10d为1疗程。观测临床症状、空腹血糖、餐后2h血糖和糖化血红蛋白、正中神经和腓总神经传导速度、不良反应。连续治疗6疗程,判定疗效。[结果]治疗组显效25例,有效15例,无效2例,总有效率为95.24%。对照组显效15例,有效13例,无效6例,总有效率为82.35%。治疗组疗效优于对照组(P<0.05)。两组血糖控制疗效均有改善(P<0.05),治疗组优于对照组(P<0.05)。两组正中神经和腓总神经传导速度均有改善(P<0.05),治疗组优于对照组(P<0.05)。[结论]针刺与自拟方联合西药治疗糖尿病周围神经病变,疗效满意,无严重不良反应,值得推广。

CONFIDENCE INTERVALS FOR NONPARAMETRIC REGRESSION FUNCTIONS WITH MISSING DATA： MULTIPLE DESIGN CASE

This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x） ＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.

Empirical likelihood inference for estimating equation with missing data

In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.

A fusion of least squares and empirical likelihood for regression models with a missing binary covariate

Multiply robust inference has attracted much attention recently in the context of missing response data. An estimation procedure is multiply robust, if it can incorporate information from multiple candidate models, and meanwhile the resulting estimator is consistent as long as one of the candidate models is correctly specified. This property is appealing, since it provides the user a flexible modeling strategy with better protection against model misspecification. We explore this attractive property for the regression models with a binary covariate that is missing at random. We start from a reformulation of the celebrated augmented inverse probability weighted estimating equation, and based on this reformulation, we propose a novel combination of the least squares and empirical likelihood to separately handle each of the two types of multiple candidate models,one for the missing variable regression and the other for the missingness mechanism. Due to the separation, all the working models are fused concisely and effectively. The asymptotic normality of our estimator is established through the theory of estimating function with plugged-in nuisance parameter estimates. The finite-sample performance of our procedure is illustrated both through the simulation studies and the analysis of a dementia data collected by the national Alzheimer's coordinating center.

Regression Analysis of Right-censored Failure Time Data with Missing Censoring Indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.

Empirical Likelihood of Quantile Difference with Missing Response When High-dimensional Covariates Are Present

We,in this paper,investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random.In particular,based on sufficient dimension reduction technique,we construct three empirical log-likelihood ratios for the quantile difference between two samples by using inverse probability weighting imputation,regression imputation as well as augmented inverse probability weighting imputation,respectively,and prove their asymptotic distributions.At the same time,we give a test to check whether two populations have the same distribution.A simulation study is carried out to investigate finite sample behavior of the proposed methods too.

Empirical Likelihood for Response Differences in Two Linear Regression Models with Missing Data

Oonsider two linear models Xi = U＇β ＋ ei, Yj = V1/2y ＋ ηj with response variables missing at random. In this paper, we assume that X, Y are missing at random （MAR） and use the inverse probability weighted imputation to produce ＇complete＇ data sets for X and Y. Based on these data sets, we construct an empirical likelihood （EL） statistic for the difference of X and Y （denoted as A）, and show that the EL statistic has the limiting distribution of X~, which is used to construct a confidence interval for A. Results of a simulation study on the finite sample performance of EL-based confidence intervals on A are reported.

Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators

The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.

Estimation for Partially Linear Models with Missing Responses:the Fixed Design Case

Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing at random（MAR）. Two types of estimators of β and g（t） for fixed t are investigated： estimators based on semiparametric regression and inverse probability weighted imputations. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on β and g（t）. Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.