Ensemble Approaches to Estimating the Population Mean with Missing Response

We propose new ensemble approaches to estimate the population mean for missing response data with fully observed auxiliary variables. We first compress the working models according to their categories through a weighted average, where the weights are proportional to the square of the least‐squares coefficients of model refitting. Based on the compressed values, we develop two ensemble frameworks, under which one is to adjust weights in the inverse probability weighting procedure and the other is built upon an additive structure by reformulating the augmented inverse probability weighting function. The asymptotic normality property is established for the proposed estimators through the theory of estimating functions with plugged‐in nuisance parameter estimates. Simulation studies show that the new proposals have substantial advantages over existing ones for small sample sizes, and an acquired immune deficiency syndrome data example is used for illustration.     

数据随机缺失下分位数回归模型的诱导光滑估计法

在数据随机缺失的分位数回归模型中,运用诱导光滑思想构造光滑的估计方程,得到了回归参数的诱导光滑估计及渐近协方差估计。接着证明了诱导光滑估计的渐近正态性质,并给出诱导光滑估计及其渐近协方差估计的算法。模拟研究表明新方法在有限样本中表现出色。     

Dimension-reduced empirical likelihood inference for response mean with data missing at random

To make efficient inference for mean of a response variable when the data are missing at random and the dimension of covariate is not low, we construct three bias-corrected empirical likelihood (EL) methods in conjunction with dimension-reduced kernel estimation of propensity or/and conditional mean response function. Consistency and asymptotic normality of the maximum dimension-reduced EL estimators are established. We further study the asymptotic properties of the resulting dimension-reduced EL ratio functions and the corresponding EL confidence intervals for the response mean are constructed. The finite-sample performance of the proposed estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.     

Inequalities for sums of squares of reranked differences involving ties and missing data

An inequality for the sum of squares of rank differences associated with Spearman’s rank correlation coefficient, when ties and missing data are present in both rankings, was established numerically in Loukas and Papaioannou (1991 Loukas, S., Papaioannou, T. (1991). Rank correlation inequalities with ties and missing data. Stat. Probab. Lett. 11:53–56.[Crossref], [Web of Science ®] , [Google Scholar]). That inequality is improved and generalized.     

Dealing with omitted answers in a survey on social integration of immigrants in Italy

ABSTRACT

Surveys are used to infer the level of social integration of immigrants. Item response theory helps to describe the relationship among responses to test items and latent traits of interest. However, in the presence of nonignorable missing data, which are omitted responses depending on the latent traits to be measured, estimates of the model parameters are biased. To account for nonignorable missing data, the quantity and quality of contacts between immigrants and natives (so called “social integration”) are taken into account through a linear function of the response propensity. Higher education, no intention to migrate again, young age, Albanian nationality, and declaring a non-Muslim religion or none, comparatively favor social integration.     

Inference and Missing Data: Asymptotic Results

In Rubin (1976) the missing at random (MAR) and missing completely at random (MCAR) conditions are discussed. It is concluded that the MAR condition allows one to ignore the missing data mechanism when doing likelihood or Bayesian inference but also that the stronger MCAR condition is in some sense the weakest generally sufficient condition allowing (conditional) frequentist inference while ignoring the missing data mechanism. In this paper it is shown that (a slightly strengthened version of) the MAR condition is sufficient to yield ordinary large sample results for estimators and test statistics and thus may be used for (asymptotic) frequentist inference.     

Pseudo likelihood-based estimation and testing of missingness mechanism function in nonignorable missing data problems

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a “synthesis" density involving the unknown missingness mechanism model and the known baseline “carrier" density in the exponential family model, we treat this “synthesis" density as a legitimate one with biased sampling version. We develop maximum pseudo likelihood estimation procedures and the resultant estimators are consistent and asymptotically normal. Since the “synthesis" cumulative distribution is a functional of the missingness mechanism model and the known carrier density, proposed method can be used to test the correctness of the missingness mechanism model nonparametrically andindirectly. Simulation studies and real example demonstrate the proposed methods perform very well.     

On estimation of frequency data with censored observations

The problem of the estimation of mean frequency of events in the presence of censoring is important in assessing the efficacy, safety and cost of therapies. The mean frequency is typically estimated by dividing the total number of events by the total number of patients under study. This method, referred to in this paper as the ‘naïve estimator’, ignores the censoring. Other approaches available for this problem require many assumptions that are rarely acceptable. These include the assumption of independence, constant hazard rate over time and other similar distributional assumptions. In this paper a simple non‐parametric estimator based on the sum of the products of Kaplan–Meier estimators is proposed as an estimator of mean frequency, and its approximate variance and standard error are derived. An illustration is provided to show the derivation of the proposed estimator. Although the clinical trial setting is used in this paper, the problem has applications in other areas where survival analysis is used and recurrent events are studied. Copyright © 2003 John Wiley & Sons, Ltd.     

Matching estimators and optimal bandwidth choice

Optimal bandwidth choice for matching estimators and their finite sample properties are examined. An approximation to their MSE is derived, as a basis for a plug-in bandwidth selector. In small samples, this approximation is not very accurate, though. Alternatively, conventional cross-validation bandwidth selection is considered and performs rather well in simulation studies: Compared to standard pair-matching, kernel and ridge matching achieve reductions in MSE of about 25 to 40%. Local linear matching and weighting perform poorly. Furthermore, the scope for developing better bandwidth selectors seems to be limited for ridge matching, but non-negligible for kernel and local linear matching.