Wouldn't It Be Nice …? The Automatic Unbiasedness of OLS (and GLS)

2008 ◽  
Vol 16 (3) ◽  
pp. 345-349 ◽  
Author(s):  
Robert C. Luskin
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Recent Issue ◽  
The Face ◽  
Best Linear Unbiased

In a recent issue of this journal, Larocca (2005) makes two notable claims about the best linear unbiasedness of ordinary least squares (OLS) estimation of the linear regression model. The first, drawn from McElroy (1967), is that OLS remains best linear unbiased in the face of a particular kind of autocorrelation (constant for all pairs of observations). The second, much larger and more heterodox, is that the disturbance need not be assumed uncorrelated with the regressors for OLS to be best linear unbiased. The assumption is unnecessary, Larocca says, because “orthogonality [of disturbance and regressors] is a property of all OLS estimates” (p. 192). Of course OLS's being best linear unbiased still requires that the disturbance be homoskedastic and (McElroy's loophole aside) nonautocorrelated, but Larocca also adds that the same automatic orthogonality obtains for generalized least squares (GLS), which is also therefore best linear unbiased, when the disturbance is heteroskedastic or autocorrelated.

scholarly journals Variation Comparison of OLS and GLS Estimators using Monte Carlo Simulation of Linear Regression Model with Autoregressive Scheme

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Sajid Ali Khan ◽  
Sayyad Khurshid ◽  
Tooba Akhtar ◽  
Kashmala Khurshid
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Small Samples ◽  
Sample Sizes

In this research we discusses to Ordinary Least Squares and Generalized Least Squares techniques and estimate with First Order Autoregressive scheme from different correlation levels by using simple linear regression model. A comparison has been made between these two methods on the basis of variances results. For the purpose of comparison, we use simulation of Monte Carlo study and the experiment is repeated 5000 times. We use sample sizes 50, 100, 200, 300 and 500, and observe the influence of different sample sizes on the estimators. By comparing variances of OLS and GLS at different values of sample sizes and correlation levels with , we found that variance of ( ) at sample size 500, OLS and GLS gives similar results but at sample size 50 variance of GLS ( ) has minimum values as compared to OLS. So it is clear that variance of GLS ( ) is best. Similarly variance of ( ) from OLS and GLS at sample size 500 and correlation -0.05 with , GLS give minimum value as compared to all other sample sizes and correlations. By comparing overall results of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS), we conclude that in large samples both are gives similar results but small samples GLS is best fitted as compared to OLS.

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

scholarly journals Extreme return, extreme volatility and investor sentiment

Filomat ◽  
2016 ◽  
Vol 30 (15) ◽  
pp. 3949-3961 ◽  
Author(s):  
Xu Gong ◽  
Fenghua Wen ◽  
Zhifang He ◽  
Jia Yang ◽  
Xiaoguang Yang ◽  
...  
Keyword(s):  
Linear Regression ◽  
Quantile Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Investor Sentiment ◽  
Generalized Least Squares ◽  
Regression Methods ◽  
Leading Role ◽  
The Impact

The extreme return and extreme volatility have great influences on the investor sentiment in stock market. However, few researchers have taken the phenomenon into consideration. In this paper, we first distinguish the extreme situations from non-extreme situations. Then we use the ordinary generalized least squares and quantile regression methods to estimate a linear regression model by applying the standardized AAII, the return and volatility of SP 500. The results indicate that, except for extremely negative return, other return sequences can cause great changes in investor sentiment, and non-extreme return plays a leading role in affecting the overall American investor sentiment. Extremely positive (negative) return can rapidly improve (further reduce) the level of investor sentiment when investors encounter extremely pessimistic situations. The impact gradually decreases with improvement of the sentiment until the situation turns optimistic. In addition, we find that extreme and non-extreme volatility cannot a_ect the overall investor sentiment.

scholarly journals ANALISIS JUMLAH KENDARAAN BERMOTOR DI DAERAH ISTIMEWA YOGYAKARTA (1990–2012)

KINERJA ◽  
2017 ◽  
Vol 19 (1) ◽  
pp. 68
Author(s):  
I Agus Wantara
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Traffic Congestion ◽  
Ordinary Least Squares ◽  
T Test ◽  
Estimation Technique ◽  
The People ◽  
Log Linear

In the last few years, traffic congestions are often occurred in Yogyakarta. This situation is caused by the increasing number of vehicles in Yogyakarta.This study evaluates the effect of the gross regional domesticproduct (PDRB), the people of Daerah Istimewa Yogyakarta (JP), and region income (PD) to the number of vehicles in Daerah Istimewa Yogyakarta (JKB). The model consists of one behavioral equation: the number of vehicles equation. The estimation technique uses Ordinary Least Squares (OLS). MacKinnon, White, and Davidson test (MWD test) is used to choose between the two models: linear regression model or log-linearregression model.The sample covers observations for 23 years (1990 - 2012). The data are obtained from (1) Bank Indonesia (2) Badan Pusat Statistik DIY and various other sources. It is found that individually lnJP andlnPD are statistically significant (positive) except ln PDRB on the basis of (separate) t test. It is also found that on the basis of the F test collectively all the regressors have a significant effect on the regressand lnJKB.Keywords: the number of vehicles, traffic congestion, linear regression model, log-linear regression model.

scholarly journals Point and interval forecasts of electricity demand with Reg-SARMA models

2021 ◽  
Author(s):  
Ilaria Lucrezia Amerise ◽  
Agostino Tarsitano
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Moving Average ◽  
Current Model ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Electricity Demand ◽  
Regression Residuals

AbstractThis paper deals especially with a two-stage approach to forecasting hourly electricity demand by using a linear regression model with serially correlated residuals. Firstly, ordinary least squares are applied to estimate a linear regression model based on purely deterministic predictors (essentially, polynomials in time and calendar dummy variables). In the case wherein the regression residuals are not a white noise series, a SARMA (seasonal autoregressive moving average) process is applied to the estimated regression residuals. After examining a vast set of potential representations, the stationary and invertible process associated with the smaller Akaike information criterion and the smaller Ljung–Box statistic is selected. Secondly, two sets of instrumental predictors are added to the current model: the estimated residuals of the first regression model plus the estimated errors of the chosen SARMA process. The new regression model is estimated by again using ordinary least squares, but taking advantage of the fact that the new regressors eliminate serial correlation. Practical issues in points and interval forecasting are illustrated with reference to nine-day ahead prediction performance for short-term electric loads in Italy.

scholarly journals A Treatise on Ordinary Least Squares Estimation of Parameters of Linear Model

2018 ◽  
Vol 7 (4.10) ◽  
pp. 518
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Linear Models ◽  
Ordinary Least Squares ◽  
Linear Estimation ◽  
Estimation Of Parameters ◽  
Parametric Function ◽  
Ols Regression

This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir.  Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.  

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