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A procedure for obtaining a robust regression employing the greatest deviation correlation coefficient

机译:利用最大偏差相关系数获得鲁棒回归的过程

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摘要

A unified approach based on correlation is developed for testing and estimation in the linear model. The correlation approach to regression offers a comprehensive framework for the simple and multiple regression setting which is elementary and homogeneous. The characteristics of the correlation coefficient determine the characteristics of the estimates.;Point estimation of the regression coefficient in Simple Linear Least Squares Regression is equivalent to finding the unique value which makes the residual vector orthogonal to the vector of observations of the regressor variable. This orthogonality condition is identical to Pearson's correlation coefficient between these vectors equalling zero. A correlation of zero for a given coefficient is a more liberal definition of orthogonal. This definition allows generation of the point estimate under any correlation coefficient. Robust point estimates of the regression coefficient result when the correlation coefficient is a robust measure of correlation such as the Greatest Deviation correlation coefficient. Point estimation of the regression coefficients in Multiple Linear Regression is the natural extension of these ideas to a system of equations. These equations are implicit functions of the regression coefficients under the Greatest Deviation correlation coefficient which require an iterative solution.;Interval estimates of the regression coefficient in Simple Linear Regression result from hypothesis tests with the test statistic as the correlation coefficient between the residual vector and the vector of observations of the regressor variable. Individual interval estimates of a regression coefficient in Multiple Linear Regression result from controlling for all other regressor variables (projection with respect to the correlation coefficient onto the subspace containing regressor of interest) and employing the hypothesis test from Simple Linear Regression.;Discussion of several examples of simple and multiple linear regression provides insight to the nature of the fits produced under the Greatest Deviation correlation coefficient and under Pearson's correlation coefficient. Regression by the Greatest Deviation correlation coefficient appears to be a practical alternative to least squares regression in all situations and preferred when the experiment contains irregular data or the normality assumptions are violated.
机译:针对线性模型中的测试和估计,开发了一种基于相关性的统一方法。回归的相关方法为基本和同质的简单多元回归设置提供了一个全面的框架。相关系数的特征决定了估计的特征。简单线性最小二乘回归中回归系数的点估计等同于找到唯一值,该唯一值使残差向量与回归变量的观测向量正交。此正交性条件等于这些向量之间的皮尔森相关系数等于零。给定系数的零相关性是对正交性的更宽泛的定义。该定义允许在任何相关系数下生成点估计。当相关系数是相关的鲁棒度量(例如最大偏差相关系数)时,将得出回归系数的鲁棒点估计。多元线性回归中回归系数的点估计是这些思想对方程系统的自然扩展。这些方程是最大偏差相关系数下回归系数的隐函数,需要迭代求解。;简单线性回归中回归系数的区间估计值来自假设检验,检验统计量为残差向量与残差向量之间的相关系数。回归变量的观测向量。通过控制所有其他回归变量(相对于包含相关回归变量的子空间上的相关系数的投影)并采用简单线性回归的假设检验,可以得出多重线性回归中回归系数的各个区间估计。简单多元线性回归分析提供了关于在最大偏差相关系数下和在Pearson相关系数下产生的拟合的性质的见解。在所有情况下,通过最大偏差相关系数进行回归似乎是最小二乘回归的一种实用替代方法,当实验包含不规则数据或违反正态性假设时,这种方法是首选方法。

著录项

  • 作者

    Rummel, Steven Eugene.;

  • 作者单位

    University of Montana.;

  • 授予单位 University of Montana.;
  • 学科 Statistics.;Mathematics.
  • 学位 Ph.D.
  • 年度 1991
  • 页码 316 p.
  • 总页数 316
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-17 11:50:27

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