On estimation of linear regression confidence bands: Analytical solution and Monte Carlo simulation

2022 ◽  
pp. 188-196
Author(s):  
A. G. Chunovkina ◽  
A. V. Stepanov ◽  
G. Wimmer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Analytical Solution ◽  
Confidence Bands

scholarly journals Confidence bands for Brownian motion and applications to Monte Carlo simulation

2007 ◽  
Vol 17 (1) ◽  
pp. 1-10 ◽  
Author(s):  
W. S. Kendall ◽  
J.-M. Marin ◽  
C. P. Robert
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Confidence Bands

scholarly journals Robustness Test of Selected Estimators of Linear Regression with Autocorrelated Error Term: A Monte-Carlo Simulation Study

2021 ◽  
pp. 1-17
Author(s):  
Rauf Ibrahim Rauf ◽  
Okoli Juliana Ifeyinwa ◽  
Haruna Umar Yahaya
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Linear Regression ◽  
Simulation Study ◽  
Explanatory Variable ◽  
Real Life ◽  
Least Square ◽  
Monte Carlo Simulation Study ◽  
Error Terms

Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.

scholarly journals Homoscedasticity: an overlooked critical assumption for linear regression

2019 ◽  
Vol 32 (5) ◽  
pp. e100148
Author(s):  
Kun Yang ◽  
Justin Tu ◽  
Tian Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Models ◽  
Data Distribution ◽  
The Other ◽  
Simulation Studies ◽  
Linear Regression Models ◽  
Popular Belief

Linear regression is widely used in biomedical and psychosocial research. A critical assumption that is often overlooked is homoscedasticity. Unlike normality, the other assumption on data distribution, homoscedasticity is often taken for granted when fitting linear regression models. However, contrary to popular belief, this assumption actually has a bigger impact on validity of linear regression results than normality. In this report, we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

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