An empirical study of PLAD regression using the bootstrap

Partial LAD regression uses the L ₁ norm associated with least absolute deviations (LAD) regression while retaining the same algorithmic structure of univariate partial least squares (PLS) regression. We use the bootstrap in order to assess the partial LAD regression model performance and to make comparisons to PLS regression. We use a variety of examples coming from NIR experiments as well as two sets of experimental data.     

我国通货膨胀的非参数回归模型

本文首先讨论非参数回归模型的局部核权最小二乘估计 ,然后建立我国通货膨胀非参数回归模型 ,最后研究了反映出口与通货膨胀关系的弹性系数     

处理多元线性回归中自变量共线性的几种方法--SAS/STAT软件(6.12)中REG等过程增强功能的使用

本文通过例子介绍多元线性回归中自变量共线性的诊断以及使用 SAS/SATA( 6.12 )软件中的 REG等过程的增强功能处理回归变量共线性的一些方法。包括筛选变量法 ,岭回归分析法 ,主成分回归法和偏最小二乘回归法     

Illustration of regression towards the means

This article, presents a procedure for generating a sequence of data sets which will yield exactly the same fitted simple linear regression equation y?=?a?+?bx. Unless rescaled, the generated data sets will have progressively smaller variability for the two variables, and the associated response and covariate will ‘regress’ towards their unconditional sample means.     

A modified candecomp algorithm for fitting the latent class model: Implementation and evaluation

In this paper an implementation is discussed of a modified CANDECOMP algorithm for fitting Lazarsfeld's latent class model. The CANDECOMP algorithm is modified such that the resulting parameter estimates are non-negative and ‘best asymptotically normal’. In order to achieve this, the modified CANDECOMP algorithm minimizes a weighted least squares function instead of an unweighted least squares function as the traditional CANDECOMP algorithm does. To evaluate the new procedure, the modified CANDECOMP procedure with different weighting schemes is compared on five published data sets with the widely-used iterative proportional fitting procedure for obtaining maximum likelihood estimates of the parameters in the latent class model. It is found that, with appropriate weights, the modified CANDECOMP algorithm yields solutions that are nearly identical with those obtained by means of the maximum likelihood procedure. While the modified CANDECOMP algorithm tends to be computationally more intensive than the maximum likelihood method, it is very flexible in that it easily allows one to try out different weighting schemes.     

Extension of multivariate regression trees to interval data. Application to electricity load profiling

Summary  Several data can be presented as interval curves where intervals reflect a within variability. In particular, this representation is well adapted for load profiles, which depict the electricity consumption of a class of customers. Electricity load profiling consists in assigning a daily load curve to a customer based on their characteristics such as energy requirement. Within the load profiling scope, this paper investigates the extension of multivariate regression trees to the case of interval dependent (or response) variables. The tree method aims at setting up simultaneously load profiles and their assignment rules based on independent variables. The extension of multivariate regression trees to interval responses is detailed and a global approach is defined. It consists in a first stage of a dimension reduction of the interval response variables. Thereafter, the extension of the tree method is applied to the first principal interval components. Outputs are the classes of the interval curves where each class is characterized both by an interval load profile (e.g. the class prototype) and an assignment rule based on the independent variables.     

Local linear regression for data with AR errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.     

Estimation for nearly unit root processes with GARCH errors

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.     

Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation

Isotonic nonparametric least squares (INLS) is a regression method for estimating a monotonic function by fitting a step function to data. In the literature of frontier estimation, the free disposal hull (FDH) method is similarly based on the minimal assumption of monotonicity. In this paper, we link these two separately developed nonparametric methods by showing that FDH is a sign-constrained variant of INLS. We also discuss the connections to related methods such as data envelopment analysis (DEA) and convex nonparametric least squares (CNLS). Further, we examine alternative ways of applying isotonic regression to frontier estimation, analogous to corrected and modified ordinary least squares (COLS/MOLS) methods known in the parametric stream of frontier literature. We find that INLS is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings. In the absence of noise, the corrected INLS (CINLS) has a higher discriminating power than FDH. In the case of noisy data, we propose to apply the method of non-convex stochastic envelopment of data (non-convex StoNED), which disentangles inefficiency from noise based on the skewness of the INLS residuals. The proposed methods are illustrated by means of simulated examples.     

Analysis of ordered categorical data from repeated measurements assuming a quantitative latent variable

Summary The purpose of the present paper is to propose an analytical method for ordered categorical responses obtained from a repeated measurement/longitudinal experiment. The ordered categorical scale is assumed to be a manifestation of a latent quantitative variable. A linear model is assumed for location parameters of the underlying distributions. Weighted least square method is applied to parameter estimation and subsequent analysis. Two data sets are analyzed to show several aspects of analysis by the proposed model and to discuss comparative characteristics of analysis compared with earlier analysis. A mention is made for a computer software program for the proposed model.     

回归分析与基于MIV的RBF神经网络在PM2.5的相关因素分析中的应用

PM2.5作为大气首要污染物,严重影响着人们的身体健康.为了研究影响PM2.5的相关指标,以武汉市的空气数据为研究对象,通过多元线性回归、偏最小二乘回归、基于MIV的RBF神经网络回归等方法对AQI中6个基本监测指标的PM2.5(含量)与其它5项分指标及其对应污染物(含量)之间的相关性进行分析;通过比较,基于MIV的RBF神经网络回归模型拟合度达到0.9302,效果最好,而且也优于BP人工神经网络回归算法,因此得出了精确可靠的影响PM2.5的指标权重大小,为减排PM2.5提供了可靠的理论依据.     

A Midpoint-Radius approach to regression with interval data

In this paper, a revisited interval approach for linear regression is proposed. In this context, according to the Midpoint-Radius (MR) representation, the uncertainty attached to the set-valued model can be decoupled from its trend. The estimated interval model is built from interval input-output data with the objective of covering all available data. The constrained optimization problem is addressed using a linear programming approach in which a new criterion is proposed for representing the global uncertainty of the interval model. The potential of the proposed method is illustrated by simulation examples.     

Bayesian networks for discrete multivariate data: an algebraic approach to inference

In this paper we demonstrate how Gröbner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gröbner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.     

线性数据拟合方法的误差分析及其改进应用

利用最小二乘法进行线性数据拟合在一定条件下存在着误差较大的缺陷,为使线性数据拟合方法在科学实验和工程实践中能够更加准确地求解量与量之间的关系表达式,本文通过对常用线性数据拟合方法———最小二乘法进行了误差分析,并在此基础上提出了最小距离平方和法以对最小二乘法作改进处理.最后,通过举例分析对两种线性数据拟合方法的优劣加以讨论并分别给出其较为合理的应用控制条件.     

r-k Class estimation in regression model with concomitant variables

We treat with the r-k class estimation in a regression model, which includes the ordinary least squares estimator, the ordinary ridge regression estimator and the principal component regression estimator as special cases of the r-k class estimator. Many papers compared total mean square error of these estimators. Sarkar (1989, Ann. Inst. Statist. Math., 41, 717–724) asserts that the results of this comparison are still valid in a misspecified linear model. We point out some confusions of Sarkar and show additional conditions under which his assertion holds.     

Nonparametric regression with current status data

We apply nonparametric regression to current status data, which often arises in survival analysis and reliability analysis. While no parametric assumption on the distributions has been imposed, most authors have employed parametric models like linear models to measure the covariate effects on failure times in regression analysis with current status data. We construct a nonparametric estimator of the regression function by modifying the maximum rank correlation (MRC) estimator. Our estimator can deal with the cases where the other estimators do not work. We present the asymptotic bias and the asymptotic distribution of the estimator by adapting a result on equicontinuity of degenerate U-processes to the setup of this paper.     

A regression model to combine results from 2 × 2 tables

A test is proposed for the comparison of two treatments with respect to a dichotomous outcome observed in several tables. The relationship of the proposed statistic to the C(α) test and to a test proposed by Radhakrishna is discussed.     

Influence function analysis applied to partial least squares

In this work we present the empirical influence functions for the covariances (eigenvalues) and directions (eigenvectors) of partial least squares under the constraint of uncorrelated components. We apply the results to several data sets and provide advice for using these tools in practice.     

Initial classification of joint data in EM estimation of latent class joint model

The latent class mixture-of-experts joint model is one of the important methods for jointly modelling longitudinal and recurrent events data when the underlying population is heterogeneous and there are nonnormally distributed outcomes. The maximum likelihood estimates of parameters in latent class joint model are generally obtained by the EM algorithm. The joint distances between subjects and initial classification of subjects under study are essential to finding good starting values of the EM algorithm through formulas. In this article, separate distances and joint distances of longitudinal markers and recurrent events are proposed for classification purposes, and performance of the initial classifications based on the proposed distances and random classification are compared in a simulation study and demonstrated in an example.     

用标准化变量方法简化介绍线性模型

用标准化变量方法,对线性回归模型的描述进行了简化,使其统计模型变得直观和容易理解.