On the convergence rate of maximal deviation distribution for kernel regression estimates

Let (X, Y), X R^p, Y R¹ have the regression function r(x) = E(Y¦X = x). We consider the kernel nonparametric estimate r_n(x) of r(x) and obtain a sequence of distribution functions approximating the distribution of the maximal deviation with power rate. It is shown that the distribution of the maximal deviation tends to double exponent (which is a conventional form of such theorems) with logarithmic rate and this rate cannot be improved.     

过两个样本点的最小一乘回归线

本文用一种选代法，求过两个样本点的最小一乘回归线．     

Empirical process of residuals for regression models with long memory errors

We consider the residual empirical process in random design regression with long memory. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for the empirical process based on (unobserved) errors.     

The breakdown behavior of the maximum likelihood estimator in the logistic regression model

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior.     

On tests for selection of variables and independence under multivariate regression models

The authors consider various procedures for testing the hypotheses of independence of two sets of variables and certain regression coefficients are zero under multivariate regression model. Various properties of these procedures and the asymptotic distributions associated with these procedures are also considered.     

A study over the general formula of regression sum of squares in multiple linear regression

In this study, in addition to the formula of regression sum of squares (SSR) in linear regression, a general formula of SSR in multiple linear regression is given. The derivations of the formula presented are given step by step. This new formula is proposed for estimation of the SSR in multiple linear regression. By using this formula, the researcher can find easily SSR and so the researcher can compose easily the table of variance analysis to interpret the regression made.     

具有线性趋势回归信度模型异方差的score检验

回归信度模型在保险研究中具有重要的作用.本文分险种内部,险种之间,险种内部及之间三种情形讨论了具有线性趋势回归信度模型异方差的score检验问题.首先推导了异方差存在性检验的score检验统计量,然后利用Monte-Carlo方法模拟了这几种检验统计量的功效,功效模拟结果显示：这几种检验统计量都有很好的检验效果.最后利用文中所得到的检验方法对旅客意外身体伤害保险数据进行了实例分析.     

利用皮尔逊分布族计算非正态分布工序能力指数

本文利用皮尔逊分布族设计了一种计算非正态分布工序能力的方法。它可用于工序分布形式完全未知的情况。     

ASYMPTOTICS OF THE RESIDUALS DENSITY ESTIMATION IN NONPARAMETRIC REGRESSION UNDER m（n）-DEPENDENT SAMPLE

Let Y_i=M(X_i)+ei, where M(x)=E(Y|X=x) is an unknown realfunction on B(? R), {(X_1,Y_i)} is a stationary and m(n)-dependent sample from(X, Y), the residuals {e_i} are independent of {X_i} and have unknown common densityf(x). In [2] a nonparametric estimate f_n(x) for f(x) has been proposed on the basisof the residuals estimates. In this paper, we further obtain the asymptotic normalityand the law of the iterated logarithm of f_n(x) under some suitable conditions. Theseresults together with those in [2] bring the asymptotic theory for the residuals densityestimate in nonparametric regression under m(n)-dependent sample to completion.     

Testing for no effect in nonparametric regression via spline smoothing techniques

We propose three statistics for testing that a predictor variable has no effect on the response variable in regression analysis. The test statistics are integrals of squared derivatives of various orders of a periodic smoothing spline fit to the data. The large sample properties of the test statistics are investigated under the null hypothesis and sequences of local alternatives and a Monte Carlo study is conducted to assess finite sample power properties.     

Quadratic mixed integer programming and support vectors for deleting outliers in robust regression

We consider the problem of deleting bad influential observations (outliers) in linear regression models. The problem is formulated as a Quadratic Mixed Integer Programming (QMIP) problem, where penalty costs for discarding outliers are used into the objective function. The optimum solution defines a robust regression estimator called penalized trimmed squares (PTS). Due to the high computational complexity of the resulting QMIP problem, the proposed robust procedure is computationally suitable for small sample data. The computational performance and the effectiveness of the new procedure are improved significantly by using the idea of ε-Insensitive loss function from support vectors machine regression. Small errors are ignored, and the mathematical formula gains the sparseness property. The good performance of the ε-Insensitive PTS (IPTS) estimator allows identification of multiple outliers avoiding masking or swamping effects. The computational effectiveness and successful outlier detection of the proposed method is demonstrated via simulated experiments. This research has been partially funded by the Greek Ministry of Education under the program Pythagoras II.     

Empirical likelihood estimators for the error distribution in nonparametric regression models

The aim of this paper is to show that existing estimators for the error distribution in non-parametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study.      

Optimizing logistic regression coefficients for discrimination and calibration using estimation of distribution algorithms

Logistic regression is a simple and efficient supervised learning algorithm for estimating the probability of an outcome or class variable. In spite of its simplicity, logistic regression has shown very good performance in a range of fields. It is widely accepted in a range of fields because its results are easy to interpret. Fitting the logistic regression model usually involves using the principle of maximum likelihood. The Newton–Raphson algorithm is the most common numerical approach for obtaining the coefficients maximizing the likelihood of the data. This work presents a novel approach for fitting the logistic regression model based on estimation of distribution algorithms (EDAs), a tool for evolutionary computation. EDAs are suitable not only for maximizing the likelihood, but also for maximizing the area under the receiver operating characteristic curve (AUC). Thus, we tackle the logistic regression problem from a double perspective: likelihood-based to calibrate the model and AUC-based to discriminate between the different classes. Under these two objectives of calibration and discrimination, the Pareto front can be obtained in our EDA framework. These fronts are compared with those yielded by a multiobjective EDA recently introduced in the literature.      

A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors

We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent estimators of the parameters—the corrected score, a structural, and the quasi-score estimators—are compared to each other with regard to their relative (asymptotic) efficiencies. The paper extends an earlier result for a scalar covariate.     

Robust placement of sensors in dynamic water distribution systems

Designing a robust sensor network to detect accidental contaminants in water distribution systems is a challenge given the uncertain nature of the contamination events (what, how much, when, where and for how long) and the dynamic nature of water distribution systems (driven by the random consumption of consumers). We formulate a set of scenario-based minimax and minimax regret models in order to provide robust sensor-placement schemes that perform well under all realizable contamination scenarios, and thus protect water consumers. Single-and multi-objective versions of these models are then applied to a real water distribution system. A heuristic solution method is applied to solve the robust models. The concept of “sensitivity region” is used to visualize trade-offs between multiple objectives.     

两个多重相关变量组的统计分析(2)

本文介绍用最小二乘准则建立多对多线性回归模型 (MLR) ,以及建立主成分回归 (PCR) ,并通过例子比较之。     

On using influence functions for testing multivariate normality

Changes in the joint distribution of influence functions for the mean vector and the covariance matrix are examined when the true probability distribution is contaminated. In particular, the formulas for influence functions of the first and second moments with respect to the above joint distribution are obtained and used to derive reasonable test statistics for multivariate normality. The formulas are extended by using the joint distribution of score functions for population parameters. An application of the extended formulas to the usual linear regression analysis leads to a measure of multivariate skewness which can be used to reduce the effect of non-normality of the response variable. Also, some relationship between the extended formulas and goodness-of-fit statistics is discussed and used to derive test statistics for multivariate normality.     

On the accuracy of empirical likelihood confidence regions for linear regression model

The coverage errors of the empirical likelihood confidence regions for in a linear regression model,Y _i=x _i+ _i , 1in, are of ordern ^–1. Bartlett corrections may be employed to reduce the order of magnitude of the coverage errors ton ^–2. For practical implementation of Bartlett correction, an empirical Bartlett correction is given.     

Robust aspects of solutions in deterministic multiple objective linear programming

We study questions of robustness of linear multiple objective problems in the sense of post-optimal analysis, that is, we study conditions under which a given efficient solution remains efficient when the criteria/objective matrix undergoes some alterations. We consider addition or removal of certain criteria, convex combination with another criteria matrix, or small perturbations of its entries. We provide a necessary and sufficient condition for robustness in a verifiable form and give two formulae to compute the radius of robustness.