拉格朗日插值多项式于平方收敛意义下的收敛逼近阶

本文得到了以 Legendre 多项式及以 Tchebycheff 多项式的导数的零点为插值结点组的拉格朗日插值多项式于平方收敛意义下的收敛速度。     

应用抽油机节能变速器实现稠油低冲次井的节能降耗

许多稠油井抽油机因为油稠、负荷重，必须采用低冲次采油，现场应用较多的是磁调速电机来调整冲次．虽然能够达到降低冲次的目的，但是电机损耗较高。抽油机节能变速器是一种针对低冲次高耗井的节能装置，是磁调速电机的替代产品。通过变速装置降低电机对抽油机变速箱的传递速度，改变电机扭矩，降低了电动机运行的均方根电流；既能达到到低冲次采油的目的，又有明显的节能效果。     

标准化系数与偏相关系数的比较与应用

在多元回归分析中，经常用标准化系数和偏相关系数来描述自变量的相对重要性，本文研究了这两个系数之间的数量关系及其统计意义，得出两者具有相同的正负号，证明出在二元回归中两者相对大小始终一致，而在自变量个数超过两个的回归模型中两者相对大小不一定完全一致，最后通过实例，说明在两者出现不一致情况下，判断自变量相对重要性的解决方法和应注意的问题。     

A Caution Regarding Rules of Thumb for Variance Inflation Factors

The Variance Inflation Factor (VIF) and tolerance are both widely used measures of the degree of multi-collinearity of the ith independent variable with the other independent variables in a regression model. Unfortunately, several rules of thumb – most commonly the rule of 10 – associated with VIF are regarded by many practitioners as a sign of severe or serious multi-collinearity (this rule appears in both scholarly articles and advanced statistical textbooks). When VIF reaches these threshold values researchers often attempt to reduce the collinearity by eliminating one or more variables from their analysis; using Ridge Regression to analyze their data; or combining two or more independent variables into a single index. These techniques for curing problems associated with multi-collinearity can create problems more serious than those they solve. Because of this, we examine these rules of thumb and find that threshold values of the VIF (and tolerance) need to be evaluated in the context of several other factors that influence the variance of regression coefficients. Values of the VIF of 10, 20, 40, or even higher do not, by themselves, discount the results of regression analyses, call for the elimination of one or more independent variables from the analysis, suggest the use of ridge regression, or require combining of independent variable into a single index.     

The one-sided Kolmogorov-Smirnov test in signal detection problems with Gaussian white noise

In this paper, we investigate the power of the Kolmogorov-Smirnov test for negativity of signals in signal detection problems with Brownian motion noise. Strict unbiasedness and admissibility are established. Moreover, taking up an approach of Häjek and Sidäk (1967) for the classical Brownian bridge case, we compute the directional derivative of the power function at the hypothesis, thus obtaining the principal direction of alternatives of the test. As an application, in a hazard rates set-up, one-sided Rényi-tests may be adjusted by choosing their weight function such that they are most sensitive against a prescribed type of alternatives. Finally, we give some numerical and simulation results.     

An application of approximate finite sample results to parameter estimation in a linear errors-in-variables model

In the simple errors-in-variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.     

外商直接投资对我国劳动生产率影响的分析

近年来,我国利用外商直接投资的步伐不断加快,外商直接投资对我国经济发展的作用越来越明显。本文通过建立计量经济学模型,定量地分析了外商直接投资对我国劳动生产率增长的贡献。     

合肥城市生活垃圾产量预测研究

通过分析合肥市城市生活垃圾产量(1994—2005年)以及影响垃圾产量的主要相关因素,采用多元回归分析方法建立了垃圾产量预测模型。分析结果表明,国内生产总值、生活消费支出和住宅使用面积是影响垃圾产量的主要因素,且都是正相关关系。采用该模型对合肥市2006—2015年生活垃圾产量进行了预测,结果显示未来十年内合肥市生活垃圾产量继续缓慢增长,预计2015年垃圾产量将达到102.61万t,人均日产量为1.42kg。