估計迴歸係數最常用的方法之一就是普通最小平方(ordinaryleastsquares)，又簡稱為最小平方法。最小平方法的「認定條件」是：Xi,i=1,2,…,n之值不為常數。除了上述認定條件之外，本章亦不對(Xi,Yi)的隨機機制作任何限制。最小平方法 找α和β使模型誤差Ui的平方和極小。採用誤差平方和是為了避免正負誤差之間...
We show a least squares estimator taking a familiar OLS/GLS expression is available in such a case. Our proposed estimator has a closed form. It can be computed without any numerical optimization and always minimizes the least squares objective function. We specify the optimally weighted GLS ...
最小平方法 可從標準方程式中求出 α和β 的解,稱作最小平方估計式 (ordinary least squares estimator,簡稱 OLS estimator),一般以 若 Xi 為常數, ,則 根本無法計算,這是為什麼需要「認定條件」的原因。 最小平方法 將最小平方估計式 代入設定的線性模型就可得到一條截距為 ,斜率為 的直線, 稱作估計的...
It is well known that the ordinary least squares estimator of X in the general linear model Ey = X, cov y = 2V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the se...
Regression model, OLS estimator, multicollinearity and type 1 error ratesThe effect of multicollinearity on the parameters of regression model using the Ordinary Least Squares (OLS) estimator is not only on estimation but also on inference. Large standard errors of the regression coefficients result ...
The paper considers the consequences of incorrectly using the ordinary least squares estimator, when the true but unknown model is a switching regression. Bias and mean square error express ons are given for slope and residual variance estimators. Except for in very specialized cases the estimators ...
Özkale MR, Kaçıranlar S (2012) Erratum to: comparisons of the \(r-k\) class estimator to the ordinary least squares estimator under the Pitmans closeness criterion. Stat pap 53(2):505–505 MATHComparisons of the r-k class estimator to the ordinary leastsquares estimator under the...
The least squares estimator minimizes e'e (the sum of squared residuals). Solving the normal equations X'Xb = X'y with respect to b yields (II.II.1-3) where X'X must be a non singular symmetric K*K matrix! Obviously, the OLS estimator is unbiased (II.II.1-4) since E(X'e) ...
Ordinary Least Squares (OLS) - ScienceDirect The OLS estimator is when the regressors are and there is no perfect , and optimal in the class of linear unbiased estimators when the are and . Under thes... ME Ezell,KC Land - 《Encyclopedia of Social Measurement》 被引量: 33发表: 2005年...
Wilcox, R. R. (2003i). Multiple hypothesis testing based on the ordinary least squares estimator when there is heteroscedasticity. Educational and Psychological Measurement, 63, 758-764.Wilcox, R. R. (2003). Multiple hypothesis testing based on the ordinary least square...