Performing armchair roundoff analyses of statistical algorithms

Numerical stability is but one of many desirable properties which should be considered when designing statistical software. However, rigorous roundoff analysis is rarely done because it seems not worth the price; the influence of rounding error is usually of secondary importance, and the analysis is thought to be beyond the reach of all but a few specialists. This note discusses the role of roundoff analysis in the design of a statistical program and shows that new techniques sometimes make assessment of the effect of rounding errors no more difficult than the verification of other program properties.     

一致光滑空间中含m-增生算子的非线性方程解的迭代程序

给出了一致光滑Banach空间中含m-增生算子的非线性方程解的带误差的Ishikawa型和Mann型迭代程序的若干收敛定理，所得的结论推广和改进了包括Liu全部定理在内的近期一些相关结果．     

RECENTERED AND RESCALED INSTRUMENTAL VARIABLE ESTIMATION OF TOBIT AND PROBIT MODELS WITH ERRORS IN VARIABLES

Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators.

This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality.     

On the usefulness of knowledge of error variances in the consistent estimation of an unreplicated ultrastructural model

This article considers an unreplicated ultrastructural model and discusses the asymptotic properties of three consistent estimators of slope parameter arising from the knowledge of measurement error variances. Conditions are deduced when knowing the error variances associated with both the study and the explanatory variables is more/less beneficial than using a single error variance in the formulation of slope estimators.     

Considerations for optimal nonparametric regression under a generalizederror structure

Nonparametric smoothing, such as kernel or spline estimation, has been examined extensively under the assumption of uncorrelated errors. This paper addresses the effects of potential correlation on consistency and other asymptotic properties in a repeated-measures model, using directly optimized linear smoothers of the replicate means. Unrestricted optimal weights, with respect to squared error loss, are used to confirm a lack of consistency for all linear estimators in an autocorrelated errors model. The results indicate kernel methods that work well for an uncorrelated errors model may not have the ability to perform satisfactorily when correlation is introduced, due to an asymmetry in the optimal weights, which disappears for an uncorrelated errors model. These would include data-driven bandwidth selection methods, adjustments of the bandwidth to accommodate correlation, higher-order kernels, and related bias reduction techniques. The analytic results suggest alternative approaches, not considered here in detail, which have shown merit.     

Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.     

CORRECTING FOR MEASUREMENT ERROR IN AN EXPOSURE-RESPONSE RELATIONSHIP BASED ON DICHOTOMISING A CONTINUOUS DEPENDENT VARIABLE

Random error in a continuous outcome variable does not affect its regression on a predictor. However, when a continuous outcome variable is dichotomised, random measurement error results in a flatter exposure-response relationship with a higher intercept. Although this consequence is similar to the effect of misclassification in a binary outcome variable, it cannot be corrected using techniques appropriate for binary data. Conditional distributions of the measurements of the continuous outcome variable can be corrected if the reliability coefficient of the measurements can be estimated. An unbiased estimate of the exposure-response relationship is then easily calculated. This procedure is demonstrated using data on the relationship between smoking and the development of airway obstruction.     

读《全隋文》札记

清人严可均编纂的《全隋文》,被誉为研究隋代文化的百科全书。但是,由于受历史条件和一人之力的局限,《全隋文》的编纂也存在着严重的缺漏和诸多失误。为了纠正此书所见失误,为研读者提供更为科学之文本,运用内、外证相结合的方法,据以文献、史籍和新出土石刻,共辑得札记23条。其中既有对录文重出互见的厘正、文字讹夺衍倒的校勘,又有文章系年的考订、补充和纠正。需要说明的是,所用《全隋文》为商务印书馆1999版,各则札记先列卷页(商务版卷数用汉字,页码用阿拉伯数字,仍依其旧),次列作者及篇名,再陈鄙见,以便检核。     

人的可靠性与人为差错

分析论述了影响人的可靠性的因素 ,提出了提高人的可靠性、减少人为差错的措施和方法。     

基于支持向量机的传感器非线性误差校正

提出了一种用支持向量机校正传感器非线性误差的原理和方法。该算法只依据样本就可以正确辩识传感器逆模型特征,而不需关于逆模型函数形式的任何先验知识,并将原问题转化为一个凸二次优化问题,能够保证找到的极值解就是全局最优解,具有较好的泛化能力。通过对电容式湿敏传感器误差校正的应用表明:该算法可取得较好的效果。