Assessing interaction effects in linear measurement error models

Summary.  In a linear model, the effect of a continuous explanatory variable may vary across groups defined by a categorical variable, and the variable itself may be subject to measurement error. This suggests a linear measurement error model with slope-by-factor interactions. The variables that are defined by such interactions are neither continuous nor discrete, and hence it is not immediately clear how to fit linear measurement error models when interactions are present. This paper gives a corollary of a theorem of Fuller for the situation of correcting measurement errors in a linear model with slope-by-factor interactions. In particular, the error-corrected estimate of the coefficients and its asymptotic variance matrix are given in a more easily assessable form. Simulation results confirm the asymptotic normality of the coefficients in finite sample cases. We apply the results to data from the Seychelles Child Development Study at age 66 months, assessing the effects of exposure to mercury through consumption of fish on child development for females and males for both prenatal and post-natal exposure.     

浅析机械工程中的虚约束

分析机械中常见的几种虚约束,说明其重要作用;由于较高的几何条件、加工和装配精度的要求,提出合理设计机构减少虚约束的方法。     

基于神经网络的六维力传感器静态标定方法研究

利用BP神经网络研究了六维力传感器的静态标定方法.良好的泛化能力是基于神经网络标定方法的关键,而现有基于神经网络的传感器标定方法对网络的泛化能力鲜有考虑.针对上述问题,以提高神经网络泛化能力为目的,对神经网络的训练样本、训练期望误差值和网络隐层单元数等的选取进行了研究.实验及计算机仿真表明,当选取样本数据具有遍历性时,利用神经网络标定后进行补偿计算可提高六维力传感器的测量精度.     

A unified empirical likelihood approach for testing MCAR and subsequent estimation

For an estimation with missing data, a crucial step is to determine if the data are missing completely at random (MCAR), in which case a complete‐case analysis would suffice. Most existing tests for MCAR do not provide a method for a subsequent estimation once the MCAR is rejected. In the setting of estimating means, we propose a unified approach for testing MCAR and the subsequent estimation. Upon rejecting MCAR, the same set of weights used for testing can then be used for estimation. The resulting estimators are consistent if the missingness of each response variable depends only on a set of fully observed auxiliary variables and the true outcome regression model is among the user‐specified functions for deriving the weights. The proposed method is based on the calibration idea from survey sampling literature and the empirical likelihood theory.     

简述宋代招标投标制度的程序

宋代的招标投标是政府与投标人之间的经济行为。招标投标制度的程序非常规范,大致可分为招标、投标、评标和定标四个环节。一般是先由官府发布招标声明,并审查投标人的资格,然后在规定的时限内收取投标文书。限满之后,在州府人员的监督下开始评标。宋代的主流评标法是最高价标准。评标结束后,要对外公布结果,官府和中标人双方签订合同,并各自履行职责。     

基于误差控制的SAR投影失真快速校正算法

随着合成孔径雷达(SAR)技术的发展和广泛应用,为了更准确反映场景信息,几何校正成为SAR图像处理过程中的重要内容.文中根据机载SAR成像机理,分析了引起机载SAR图像几何投影失真的原因,并估算出其失真量,针对传统的非线性校正方法,提出了一种快速高效的基于误差控制的动态分段线性校正算法.该算法在保证SAR图像校正质量的前提下,通过控制SAR图像校正误差,用线性处理取代了非线性逐点运算,使得校正算法的计算复杂度大大降低.文中还从理论上推导出最佳的分段校正长度计算方法,可校正过程中动态调整分段长度,保证校正质量和运算效率.最后通过仿真试验验证了该文法的有效性和实用性.     

Errors-in-variables beta regression models

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0, 1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The structural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the naïve estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.     

Total least squares and bootstrapping with applications in calibration

The solution to the errors-in-variables problem computed through total least squares is highly nonlinear. Because of this, many statistical procedures for constructing confidence intervals and testing hypotheses cannot be applied. One possible solution to this dilemma is bootstrapping. A nonparametric bootstrap technique could fail. Here, the proper nonparametric bootstrap procedure is provided and its correctness is proved. On the other hand, a residual bootstrap is not valid and suitable in this case. The results are illustrated through a simulation study. An application of this approach to calibration data is presented.     

Mixture Distributions Based Methods of Calibration for the Empirical Log-Likelihood Ratio

Empirical likelihood ratio confidence regions based on the chi-square calibration suffer from an undercoverage problem in that their actual coverage levels tend to be lower than the nominal levels. The finite sample distribution of the empirical log-likelihood ratio is recognized to have a mixture structure with a continuous component on [0, + ∞) and a point mass at + ∞. The undercoverage problem of the Chi-square calibration is partly due to its use of the continuous Chi-square distribution to approximate the mixture distribution of the empirical log-likelihood ratio. In this article, we propose two new methods of calibration which will take advantage of the mixture structure; we construct two new mixture distributions by using the F and chi-square distributions and use these to approximate the mixture distributions of the empirical log-likelihood ratio. The new methods of calibration are asymptotically equivalent to the chi-square calibration. But the new methods, in particular the F mixture based method, can be substantially more accurate than the chi-square calibration for small and moderately large sample sizes. The new methods are also as easy to use as the chi-square calibration.     

Conditional multivariatk calibration

The problem of simple linear calibration is not new and dates back to the late 1930's. In 1982 Brown presented a number of important results for the multivariate case. In this paper we extend Brown's work to cover the situation where one is interested in calibrating for an unknown q-vector X on the basis of an observed p-vector Y given that k≥l components of X are fixed in advance.

An outline of the theoretical development in the multivariate normal case will be given and the procedure illustrated with the application to previously published data.