Partitioned Ridge Regression

In this paper we examine the relationship between the general ridge estimator and the standardized ridge estimator.     

A Note on a Regression Transformation for Smaller Round-Off Error

This paper describes transformations of regression data that result in certain zero off-diagonal elements in the correlation matrix and hence decrease the adverse effect of round-off error in the inversion of the matrix in least-squares solutions.     

A Note on Shortest Prediction Intervals for Log-Linear Regression

Analytical and Monte Carlo results are used to investigate the robustness of the exact statistical test suggested by Nelson for testing the hypothesis of equality of two availabilities. A non-parametric test based on a generalized U-statistic is proposed which does not depend on the assumption that the times to failure and times to repair are exponentially distributed. Additional Monte Carlo results are used to point out the strengths and weaknesses of this test.     

A Comment on Ridge Regression. Biased Estimation for Non-Orthogonal Problems

In a recent issue of Technometrics, Hoer1 and Kennard [l] presented a comprehensive discussion of the problem of biased estimation in multiple regression that fits into the general linear hypothesis model of full rank. An alternative characterization of the form of the biased estimator has been presented in this note, and an “existence theorem” proven indicating that there exists a k such that the biased estimation based on the proposed characterization would still lead to increased accuracy.     

Centering and Scaling in Ridge Regression

A simple generalization of the usual ridge regression estimator for the linear regression model is given which avoids the need to center all variables. The estimator is proved to be location invariant. This estimator is of pedagogical interest and in forecasting also of practical importance.     

A Note on the Application of Davidon's Method to Nonlinear Regression Problems

A sequential procedure is given for selecting from a given multinomial distribution with k cells, the cell with the largest probability, which is called the “most probable” category. Observations being taken sequentially from the given distribution, the sampling is terminated when the difference between the highest and the next highest cell counts is equal to a positive integer r. The cell with the highest count when the sampling is terminated, is selected as the most probable category. It is shown that the sampling terminates with probability 1. The probability of a correct selection and the expected total number of observations are given. The given procedure is compared with other known procedures.     

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.     

Classical F-Tests and Confidence Regions for Ridge Regression

For testing general linear hypotheses in multiple regression models. it is shown that non-stochastically shrunken ridge estimators yield the same central F-ratios and t-statistics as does the least squares estimator. Thus although ridge regression does produce biased point estimates which deviate from the least squares solution, ridge techniques do not generally yield “new” normal theory statistical inferences: in particular, ridging does not necessarily produce “shifted” confidence regions. A concept, the ASSOCIATFD PROBABILITY of a ridge estimate, is defined using the usual, hyperellipsoidal confidence region centered at the least squares estimator, and it is argued that ridge estimates are of relatively little interest when they are so “extreme” that they lie outside of the least squares region of say 90 percent confidence.     

Note on Procedures for Variable Selection in Multiple Regression

Mantel (1970) has pointed out that many procedures are now available for selecting variables in multiple regression analyses. This note reviews the more important ones briefly, and suggests that Mantel exaggerates the advantages of the backward elimination or %tepdown” procedure.     

PC准则下生长曲线模型回归参数阵岭估计的优良性

将 PC准则推广应用于生长曲线模型参数阵的最小二乘估计和岭估计优劣性的比较 ,给出了岭估计在PC准则下优于最小二乘估计的条件     

Diabetes Prediction Algorithm Using Recursive Ridge Regression L2

At present, the prevalence of diabetes is increasing because the human body cannot metabolize the glucose level. Accurate prediction of diabetes patients is an important research area. Many researchers have proposed techniques to predict this disease through data mining and machine learning methods. In prediction, feature selection is a key concept in preprocessing. Thus, the features that are relevant to the disease are used for prediction. This condition improves the prediction accuracy. Selecting the right features in the whole feature set is a complicated process, and many researchers are concentrating on it to produce a predictive model with high accuracy. In this work, a wrapper-based feature selection method called recursive feature elimination is combined with ridge regression (L2) to form a hybrid L2 regulated feature selection algorithm for overcoming the overfitting problem of data set. Overfitting is a major problem in feature selection, where the new data are unfit to the model because the training data are small. Ridge regression is mainly used to overcome the overfitting problem. The features are selected by using the proposed feature selection method, and random forest classifier is used to classify the data on the basis of the selected features. This work uses the Pima Indians Diabetes data set, and the evaluated results are compared with the existing algorithms to prove the accuracy of the proposed algorithm. The accuracy of the proposed algorithm in predicting diabetes is 100%, and its area under the curve is 97%. The proposed algorithm outperforms existing algorithms.     

岭回归协助稀疏表示红外小目标检测

提出一种基于岭回归协助稀疏表示的红外小目标检测方法。该方法分别采用二维高斯模型和正态分布随机矩阵生成红外小目标样本和背景样本,继而建立超完备字典。红外小目标检测包括两个阶段,在第一阶段利用岭回归表示快速计算所有测试样本的岭回归重建误差;在第二阶段,根据岭回归重建误差自适应选择候选目标,并计算其稀疏表示重建误差实现目标检测。对提出的方法进行了实验验证,结果表明:提出的方法具有较快的速度和较强的鲁棒性。     

A Note on Fullerenes

The existence of fullerenes with any number of hexagons different from 1 is proven in a simple way.     

Firework Plots for Evaluating the Impact of Outliers and Influential Observations in Ridge Regression

With many predictors in regression, fitting the full model can induce multicollinearity problems. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Outliers can distort many measures in data analysis and statistical modeling, while influential points can have disproportionate impact on the estimated values of model parameters. Graphical summaries, called firework plots, are simple tools for evaluating the impact of outliers and influential points in regression. Variations of the plots focus on allowing visualization of the impact on the estimated parameters and variability. This paper describes how three‐dimensional and pairwise firework plots as well as scalable waterfall–firework plots can be used to increase understanding of contributions of individual observations and as a complement to other regression diagnostic techniques in the ridge regression setting. Using these firework plots, we can find outliers and influential points and their impact on model parameters and show how in some applications, the type of analysis used changes the impact of various observations. We illustrate the methods with two examples. Copyright © 2016 John Wiley & Sons, Ltd.     

A Note on “Capability Assessment for Processes with Multiple Characteristics: A Generalization of the Popular Index Cpk”

The generalized yield index establishes the relationship between the manufacturing specifications and the actual process performance, which provides a lower bound on process yield for two‐sided processes with multiple characteristics. The results attended are very practical for industrial application. In this article, we extended the results in cases with one‐sided specification and multiple characteristics. The generalized index was considered, and the asymptotic distribution of the natural estimator was developed. Then, we derived the lower confidence bounds as well as the critical values of index . We not only provided some tables but also presented an application example. Copyright © 2012 John Wiley & Sons, Ltd.     

关于Wiener过程增量的注

本文讨论Ｗｉｅｎｅｒ过程增量的下极限结果找到正则因子ｄ（Ｔ,ｔ）,使得ｓｕｐａＴ≤ｔ≤Ｔｓｕｐｔ≤ｓ≤Ｔｄ（Ｔ,ｔ）｜ｗ（ｓ）－ｗ（ｓ－ｔ）｜与ｓｕｐｓＴ≤ｔ≤Ｔｓｕｐｔ≤ｓ≤Ｔｓｕｐ０≤ｂ≤ｔｄ（Ｔ,ｔ）｜ｗ（ｓ）－ｗ（ｓ－ｈ）｜的下极限１。     

关于一类Bernoulli随机变量研究的一个注记

本文给出了一类Bernoulli随机变量特征函数列收敛的一个等价条件．