Comparison of Two Estimation Methods of Missing Values Using Pitman-Closeness Criterion

In this article, a proof is given that the linear interpolator is Pitman-closer than the linear predictor with respect to a missing value of a stationary first-order autoregressive process.     

Use of robust estimators of missing data in evaluating shiftwork performance

Abstract

Major problems apparent in studies evaluating the performance of employees across a large number of shifts often involve data missing due to a lack of employee participation in all possible shifts, and large variance around central tendency estimators owing to extreme responses on performance measures. These problems and possible solutions are considered here with reference to a data set collected from a number of shiftworkers in the steel industry. Data were collected from 28 employees over a morning shift and night-shift roster. The shift consisted of two cycles of MORNING-MORNING-NIGHT-NIGHT. The employees were male computer operators working a 12-h shift. The work required them to be constantly alert, and to read, monitor and respond to messages from multiple media channels. Included in the test battery were five performance indicators of cognitive speed and power. This battery was delivered using two IBM computers, which controlled the sequences and administration of the cognitive tasks. Administration of the battery was conducted in the work room and undertaken as close as possible to starting work, and as close as possible to completing work. The findings indicate that regression modelling was the most efficient way of estimating missing data. The use of M-estimators reduced the influence of extreme values on parameter estimation, and increased effect size over that observed using raw data.     

Multiple imputation for continuous variables using a Bayesian principal component analysis

ABSTRACT

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the PCA model. Using a simulation study and real data sets, the method is compared to two classical approaches: multiple imputation based on joint modelling and on fully conditional modelling. Contrary to the others, the proposed method can be easily used on data sets where the number of individuals is less than the number of variables and when the variables are highly correlated. In addition, it provides unbiased point estimates of quantities of interest, such as an expectation, a regression coefficient or a correlation coefficient, with a smaller mean squared error. Furthermore, the widths of the confidence intervals built for the quantities of interest are often smaller whilst ensuring a valid coverage.     

测量误差模型稳健方法及应用研究

回归模型在经济学、生物医学、流行病学、工农业生产等众多领域有着广泛的应用,而在实际数据收集时常常出现无法获得变量的精确数据或全部数据的情况,即常碰到测量误差数据、缺失数据等复杂数据情形。对于回归模型中存在测量误差的情况,如在参数估计时不加以修正,则易产生估计偏差,使得估计精度下降。对于数据缺失情形,如不采取合理的处理方法也会导致模型分析结果不佳。故此,本文研究含有测量误差数据时,解释变量具有随机缺失时的线性测量误差模型和部分线性测量误差模型的稳健参数估计问题。本文提出了一种在测量误差服从拉普拉斯分布时参数的损失修正估计,通过蒙特卡洛模拟和医学研究中的实证分析,显示本文所提的估计方法具有偏差小、精度高、稳健性强的优势。     

Power of double-sampling tests for General Linear Hypotheses

In this paper, testing procedures based on double-sampling are proposed that yield gains in terms of power for the tests of General Linear Hypotheses. The distribution of a test statistic, involving both the measurements of the outcome on the smaller sample and of the covariates on the wider sample, is first derived. Then, approximations are provided in order to allow for a formal comparison between the powers of double-sampling and single-sampling strategies. Furthermore, it is shown how to allocate the measurements of the outcome and the covariates in order to maximize the power of the tests for a given experimental cost.     

EM Algorithm Estimation of Simultaneous Equation Model with Limited Variables: An Example of Cigarette Consumption

The two-part model and Heckman's sample selection model are often used in economic studies which involve analyzing the demand for limited variables. This study proposed a simultaneous equation model (SEM) and used the expectation-maximization algorithm to obtain the maximum likelihood estimate. We then constructed a simulation to compare the performance of estimates of price elasticity using SEM with those estimates from the two-part model and the sample selection model. The simulation shows that the estimates of price elasticity by SEM are more precise than those by the sample selection model and the two-part model when the model includes limited independent variables. Finally, we analyzed a real example of cigarette consumption as an application. We found an increase in cigarette price associated with a decrease in both the propensity to consume cigarettes and the amount actually consumed.     

Sparse Functional Principal Component Analysis via Regularized Basis Expansions and Its Application

This article introduces principal component analysis for multidimensional sparse functional data, utilizing Gaussian basis functions. Our multidimensional model is estimated by maximizing a penalized log-likelihood function, while previous mixed-type models were estimated by maximum likelihood methods for one-dimensional data. The penalized estimation performs well for our multidimensional model, while maximum likelihood methods yield unstable parameter estimates and some of the parameter estimates are infinite. Numerical experiments are conducted to investigate the effectiveness of our method for some types of missing data. The proposed method is applied to handwriting data, which consist of the XY coordinates values in handwritings.     

Estimating Transition Probabilities for Ignorable Intermittent Missing Data in a Discrete-Time Markov Chain

This article considers a discrete-time Markov chain for modeling transition probabilities when multiple successive observations are missing at random between two observed outcomes using three methods: a na\"?ve analog of complete-case analysis using the observed one-step transitions alone, a non data-augmentation method (NL) by solving nonlinear equations, and a data-augmentation method, the Expectation-Maximization (EM) algorithm. The explicit form of the conditional log-likelihood given the observed information as required by the E step is provided, and the iterative formula in the M step is expressed in a closed form. An empirical study was performed to examine the accuracy and precision of the estimates obtained in the three methods under ignorable missing mechanisms of missing completely at random and missing at random. A dataset from the mental health arena was used for illustration. It was found that both data-augmentation and nonaugmentation methods provide accurate and precise point estimation, and that the na\"?ve method resulted in estimates of the transition probabilities with similar bias but larger MSE. The NL method and the EM algorithm in general provide similar results whereas the latter provides conditional expected row margins leading to smaller standard errors.     

Estimators for the Population Mean in the Case of Missing Data

We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555–579.[Crossref], [Web of Science ®] , [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.     

Stratified Logrank Test of No Randomized Treatment Effect with Missing Stratum Information

A major objective in many clinical trials is to compare several competing treatments in a randomized experiment. In such studies, it is often necessary to adjust for some other important factor that affects the event rates in the treatment groups. When this factor is discrete, one usual approach uses a stratified version of the logrank test. In this article, we consider the problem that arises when the factor giving rise to the strata is missing at random for some of the study subjects. This article proposes a modified version of the stratified logrank test, in which the unobserved stratum indicators are replaced by an estimate of their conditional expectation given available auxiliary covariate measurements. The null asymptotic distribution of the proposed test statistic is investigated. Simulation experiments are also conducted to examine the finite-sample behavior of this test under both null and alternative hypotheses. Simulations indicate that the proposed test performs well, even under some moderate deviations to the at-random missingness assumption.