Measurement Error Correction by Exploiting Gene–Environment Independence in Family‐Based Case–Control Studies

Abstract. Family‐based case–control designs are commonly used in epidemiological studies for evaluating the role of genetic susceptibility and environmental exposure to risk factors in the etiology of rare diseases. Within this framework, it is often reasonable to assume genetic susceptibility and environmental exposure being conditionally independent of each other within families in the source population. We focus on this setting to explore the situation of measurement error affecting the assessment of the environmental exposure. We correct for measurement error through a likelihood‐based method. We exploit a conditional likelihood approach to relate the probability of disease to the genetic and the environmental risk factors. We show that this approach provides less biased and more efficient results than that based on logistic regression. Regression calibration, instead, provides severely biased estimators of the parameters. The comparison of the correction methods is performed through simulation, under common measurement error structures.     

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.     

A family of estimators of population variance in two-occasion rotation patterns

Abstract

In this article, we have considered the problem of estimation of population variance on current (second) occasion in two occasion successive (rotation) sampling. A class of estimators of population variance has been proposed and its asymptotic properties have been discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion and the Singh et al. (2013) estimator. Optimum replacement policy is discussed. It has been shown that the suggested estimator is more efficient than the Singh et al. (2013) estimator and a usual unbiased estimator when there is no matching. An empirical study is carried out in support of the present study.     

A Semiparametric Approach for Accelerated Failure Time Models with Covariates Subject to Measurement Error

There are relatively few discussions about measurement error in the accelerated failure time (AFT) model, particularly for the semiparametric AFT model. In this article, we propose an adjusted estimation procedure for the semiparametric AFT model with covariates subject to measurement error, based on the profile likelihood approach and simulation and exploration (SIMEX) method. The simulation studies show that the proposed semiparametric SIMEX approach performs well. The proposed approach is applied to a coronary heart disease dataset from the Busselton Health study for illustration.     

混合学习法前向网络多属性储层参数预测

应用前向网络描述地震属性和储层参数间的非线性映射关系时，经典的误差反向传播算法存在收敛速度慢，易陷入局部极值等诸多不足。研究了融合粒子群优化算法和误差反向传播算法的混合学习法前向网络多属性储层参数预测技术。粒子群优化算法是一种群体随机搜索演化计算技术，具有较快的收敛速度和较强的全局搜寻能力；误差反向传播算法本质上是梯度下降算法，注重局部搜索。混合学习法为两种学习算法交替执行，首先以粒子群优化算法训练网络，当误差能量在规定的迭代次数内不再发生变化时，采用误差反向传播算法实现局部寻优。理论函数逼近测试和实际储层参数预测实验说明了混合学习法具有学习时间短、求解效率高、可靠性强的优点，具有良好的应用前景。     

A robust procedure for testing an assumed value of the population correlation coefficient

For testing that the population correlations coefficientp Q, Tiku and Balakrishnan1986) developed a robust test. This test is extended here to situcitions where one wants to test that p p , p being a specified non-zero value of p. o o     

An alternative approach to variable selection for prediction

A procedure for selecting a subset of predictor variables in regression analysis is suggested. The procedure is so designed that it leads to the selection of a subset of variables having an adequate degree of informativeness with a directly specified confidence coefficient. Some examples are considered to illustrate the application of the procedure.     

Use of several auxiliary variables in estimating the population mean in a two-occasion rotation pattern

ABSTRACT

This paper addresses the problem of estimation of the population mean on the current (second) occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on the study variable from the previous occasion, an estimation procedure of the population mean on the current occasion has been proposed. Theoretical properties of the proposed estimator have been investigated. Optimum replacement policy to the proposed estimator has been discussed. The proposed estimator has been compared empirically with the sample mean estimator, when there is no matching and the optimum estimator which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion. Appropriate recommendations have been made for practical applications.     

Measurement error in regression analysis

Consider the linear regression model Y = Xθ+ ε where Y denotes a vector of n observations on the dependent variable, X is a known matrix, θ is a vector of parameters to be estimated and e is a random vector of uncorrelated errors. If X'X is nearly singular, that is if the smallest characteristic root of X'X s small then a small perurbation in the elements of X, such as due to measurement errors, induces considerable variation in the least squares estimate of θ. In this paper we examine for the asymptotic case when n is large the effect of perturbation with regard to the bias and mean squared error of the estimate.     

A Novel Human Error Probability Assessment Using Fuzzy Modeling

Human error is one of the significant factors contributing to accidents. Traditional human error probability (HEP) studies based on fuzzy number concepts are one of the contributions addressing such a problem. It is particularly useful under circumstances where the lack of data exists. However, the degree of the discriminability of such studies may be questioned when applied under circumstances where experts have adequate information and specific values can be determined in the abscissa of the membership function of linguistic terms, that is, the fuzzy data of each scenario considered are close to each other. In this article, a novel HEP assessment aimed at solving such a difficulty is proposed. Under the framework, the fuzzy data are equipped with linguistic terms and membership values. By establishing a rule base for data combination, followed by the defuzzification and HEP transformation processes, the HEP results can be acquired. The methodology is first examined using a test case consisting of three different scenarios of which the fuzzy data are close to each other. The results generated are compared with the outcomes produced from the traditional fuzzy HEP studies using the same test case. It is concluded that the methodology proposed in this study has a higher degree of the discriminability and is capable of providing more reasonable results. Furthermore, in situations where the lack of data exists, the proposed approach is also capable of providing the range of the HEP results based on different risk viewpoints arbitrarily established as illustrated using a real‐world example.