Note on a Distribution-free CUSUM Technique

A cumulative sum technique which allows distribution-free tests is developed and applied to the problem of detecting a change in median of a rainfall distribution.     

An Adaptive,Automatic Multiple-Case Deletion Technique for Detecting Influence in Regression

Critical to any regression analysis is the identification of observations that exert a strong influence on the fitted regression model. Traditional regression influence statistics such as Cook's distance and DFFITS, each based on deleting single observations, can fail in the presence of multiple influential observations if these influential observations “mask” one another, or if other effects such as “swamping” occur. Masking refers to the situation where an observation reveals itself as influential only after one or more other observations are deleted. Swamping occurs when points that are not actually outliers/influential are declared to be so because of the effects on the model of other unusual observations. One computationally expensive solution to these problems is the use of influence statistics that delete multiple rather than single observations. In this article, we build on previous work to produce a computationally feasible algorithm for detecting an unknown number of influential observations in the presence of masking. An important difference between our proposed algorithm and existing methods is that we focus on the data that remain after observations are deleted, rather than on the deleted observations themselves. Further, our approach uses a novel confirmatory step designed to provide a secondary assessment of identified observations. Supplementary materials for this article are available online.     

回归模型的建立——回归分析在陶瓷多元系中的应用

以确定普通陶瓷坯体的烧结温度与化学组成之间的定量关系为研究目标，结合基本的工艺原理探讨如何建立适宜的回归模型，从而合理的应用多元回归分析得出正确的回归方程。     

自适应光学系统中实时自适应控制的仿真研究

介绍和分析了一种利用校正残差进行实时迭代的自适应控制算法，可以应用到校正大气湍流的实际自适应光学系统。利用61单元自适应光学系统上实际采集的大气湍流扰动信号，实现了自适应控制算法，并对这种算法的收敛性、稳定性、控制效果等进行了计算机仿真研究，与常规PID算法进行了比较。     

Convergence in Nonlinear Regression

Least squares estimates of parameters of a multiple linear regression model are known to be highly variable when the matrix of independent variables is near singular. Using the latent roots and latent vectors of the “correlation matrix” of the dependent and independent variables a modified least squares estimation procedure is introduced. This technique enables one to determine whether the near singularity has predictive value and examine alternate prediction equations in which the effect of the near singrtlarity has been removed from the estimates of the regression coefficients. In addition a method for performing backward elimination of variables using standard least squares or the modified procedure is presented.     

光电技术研究所的自适应光学技术

自适应光学是近二十年发展起来的光学新技术，它使光学系统具有能动地适应外界变化自动克服动态干扰的能力。十多年来光电技术研究所的自适应光学研究室建立了自适应光学技术的基础，研制成功多套自适应光学系统。带动了能动光学元件、微驱动技术和光束动态诊断技术等单元技术的发展。本文综合报导了这些技术进展。     

整群抽样回归估计量

研究了有辅助指标的整群抽样，构造了总体总值的回归估计量，证明了回归估计量是可用的，并且不劣于整群抽样下的简单估计量及整群抽样下的比估计量。     

Self Modeling Nonlinear Regression

The paper is concerned with parametric models for populations of curves; i.e. models of the form y_i (Z) = f(θ _i ; x) + error, i = I, 2, …, n. The shape invariant model f(θ _i ; x) = θ_0i + θ_1i g([x – θ_2i /θ_3i ) is introduced. If the function g(x) is known, then the θ _i may be estimated by nonlinear regression. If g(x) is unknown, then the authors propose an iterative technique for simultaneous determination of the best g(x) and θ _i . Generalizations of the shape invariant model to curve resolution are also discussed. Several applications of the method are also presented.     

A Robust Method for Multiple Linear Regression

Techniques of fitting are said to be resistant when the result is not greatly altered in the case a small fraction of the data is altered: techniques of fitting are said to be robust of efficiency when their statistical efficiency remains high for conditions more realistic than the utopian cases of Gaussian distributions with errors of equal variance. These properties are particularly important in the formative stages of model building when the form of the response is not known exactly. Techniques with these properties are proposed and discussed.     

A Nonparametric Adaptive Sampling Strategy for Online Monitoring of Big Data Streams

With the rapid advancement of sensor technology, a huge amount of data is generated in various applications, which poses new and unique challenges for statistical process control (SPC). In this article, we propose a nonparametric adaptive sampling (NAS) strategy to online monitor nonnormal big data streams in the context of limited resources, where only a subset of observations are available at each acquisition time. In particular, this proposed method integrates a rank-based CUSUM scheme and an innovative idea that corrects the anti-rank statistics with partial observations, which can effectively detect a wide range of possible mean shifts when data streams are exchangeable and follow arbitrary distributions. Two theoretical properties on the sampling layout of the proposed NAS algorithm are investigated when the process is in control and out of control. Both simulations and case studies are conducted under different scenarios to illustrate and evaluate the performance of the proposed method. Supplementary materials for this article are available online.     

An Explicit Solution for Generalized Ridge Regression

The general form of ridge regression proposed by Hoerl and Kennard is examined in the context of the iterative procedure they suggest for obtaining optimal estimators. It is shown that a non-iterative, closed form solution is available for this procedure. The solution is found to depend upon certain convergence/divergence conditions which relate to the ordinary least) squares estimators. Numerical examples are given.     

Matrices With Applications in Statistics

Sample size determination methods are considered for hypothesis testing about location parameters of two continuous distributions using independent random samples and the Mann–Whitney–Wilcoxon (MWW) test, for a specified shift, size, and power. These methods are based on the so-called “Noether's formula,” derived from a normal approximation to the power of the MWW test, and a pilot sample from each of the distributions. Compared with alternate methods, including the one using bootstrap similar to that of Hamilton and Collings (1991) the new methods are shown to be at least as good in terms of accuracy and substantially more efficient in terms of speed and variability. The simpler method, using linearly smoothed empirical cdf's of the pilot samples and requiring no bootstrapping, is recommended for practical use. Extensions and adaptations for obtaining an upper confidence bound on the sample size and to general linear rank tests are indicated.     

低浓度样品测定时回归曲线中截距的处理

截距对低浓度样品计算却影响甚大,尤其是当样品浓度接近空白浓度时,用线性回归方程计算时会出现偏差。通过计算统计量判定回归曲线是否过原点、计算容许值判定离群值是否异常及通过Origin的线性拟合功能强制过原点,可以有效避免因线性拟合过程中导致的计算误差,从而保证低浓度样品测定结果的准确性。     

Choice of Levels in Polynomial Regression with One or Two Variables

Suggested levels for the independent variables are tabled for polynomial regression in one variable and for two particular polynomial regressions in two independent variables when the minimum number of distinct levels is used. The criterion used for finding these levels was restricted minimization of the generalized variance. An explanation of the usefulness of this criterion is given, and a computational method is outlined to find levels for other regression equations using this criterion.     

Classical and Inverse Regression Methods of Calibration

The Classical and Inverse least squares methods of linear calibration are compared by Monte Carlo methods. The Inverse approach is found to be superior to the Classical approach from a mean squared error point of view.