Classification with discrete and continuous variables via general mixed-data models

We study the problem of classifying an individual into one of several populations based on mixed nominal, continuous, and ordinal data. Specifically, we obtain a classification procedure as an extension to the so-called location linear discriminant function, by specifying a general mixed-data model for the joint distribution of the mixed discrete and continuous variables. We outline methods for estimating misclassification error rates. Results of simulations of the performance of proposed classification rules in various settings vis-à-vis a robust mixed-data discrimination method are reported as well. We give an example utilizing data on croup in children.     

Proportion estimation in mixtures with covariates

Linear maps of a single unclassified observation are used to estimate the mixing proportion in a mixture of two populations with homogeneous variances in the presence of covariates. with complete knowledge of the parameters of the individual populations, the linear map for which the estimator is unbiased and has minimum variance amongst all similar estimators can be determined. Plug-in estimator based on independent training samples from the component populations can be constructed and is asymptotically equivalent to Cochran's classification statistic V* for covariate classification; see Memon and Okamoto (1970). Under normality assumptions, asymptotic expansion of the distribution of the plug-in estimator is available. In the absence of covariates, our estimator reduces to that suggested by Walker (1980) who has investigated the problem based on information on large unclassified samples from a mixture of two populations with heterogeneous variances. In contrast, distribution of Walker's estimator seems intractable in moderate sample sizes even with normality assumption.     

Bootstrap Bandwidth Selection Using an h-Dependent Pilot Bandwidth

Abstract.  The problem of choosing the bandwidth h for kernel density estimation is considered. All the plug-in-type bandwidth selection methods require the use of a pilot bandwidth g . The usual way to make an h -dependent choice of g is by obtaining their asymptotic expressions separately and solving the two equations. In contrast, we obtain the asymptotically optimal value of g for every fixed h , thus making our selection 'less asymptotic'. Exact error expressions show that some usually assumed hypotheses have to be discarded in the asymptotic study in this case. Two versions of a new bandwidth selector based on this idea are proposed, and their properties are analysed through theoretical results and a simulation study.     

Boundary Aware Estimators of Integrated Density Derivative Products

Integrated squared density derivatives are important to the plug-in type of bandwidth selector for kernel density estimation. Conventional estimators of these quantities are inefficient when there is a non-smooth boundary in the support of the density. We introduce estimators that utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean-squared error that are familiar from non-boundary cases, and the constant coefficients have similar forms. The estimators and the formula for their asymptotically optimal bandwidths, which depend on integrated products of density derivatives, are applied to automatic bandwidth selection for local linear density estimation. Simulation studies show that the constructed bandwidth rule and the Sheather–Jones bandwidth are competitive in non-boundary cases, but the former overcomes boundary problems whereas the latter does not.     

Estimation of the signal-to-noise in the linear regression model

In the present paper estimators of the signal-to-noise are given. A simulation study is conducted in order to see how the proposed estimators perform relative to the naive estimator by way of scalar risk comparison. The results favour our suggested estimators.     

基于AutoCAD的钣金自动展开及排样优化

针对传统钣金生产过程中的效率低下、精度不高、材料浪费等缺点,提出基于CAD自动化技术的钣金展开及排 样优化应用系统,设计了系统的整体流程结构;借助于旋转最低水平线的遗传算法、最小矩形包络法和平移靠接算法为 核心,分别处理规则矩形和不规则矩形的排样优化问题。开发了基于AutoCAD应用平台的钣金展开及排样优化的插件 系统,该系统主要由参数化绘图、三维图显示、确定图幅及尺寸精度等功能组成;最后通过实例应用,表明该系统能有效 提高钣金生产的效率和制造精度,降低材料浪费率。