scholarly journals Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study

2021 ◽  
Vol 2 (1) ◽  
pp. 26-39
Author(s):  
Sajid Ali Khan ◽  
Sayyad Khurshid ◽  
Shabnam Arshad ◽  
Owais Mushtaq
Keyword(s):  
Sample Size ◽  
Least Squares ◽  
Small Sample Size ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Small Sample ◽  
Correlated Errors ◽  
Bias Estimation ◽  
Gls Estimation ◽  
Correlation Level

In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.

Nuisance vs. Substance: Specifying and Estimating Time-Series-Cross-Section Models

1996 ◽  
Vol 6 ◽  
pp. 1-36 ◽  
Author(s):  
Nathaniel Beck ◽  
Jonathan N. Katz
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Cross Section ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Correlated Errors ◽  
Section Data ◽  
Variable Approach ◽  
Parameter Heterogeneity ◽  
Lagged Dependent Variable

In a previous article we showed that ordinary least squares with panel corrected standard errors is superior to the Parks generalized least squares approach to the estimation of time-series-cross-section models. In this article we compare our proposed method with another leading technique, Kmenta's “cross-sectionally heteroskedastic and timewise autocorrelated” model. This estimator uses generalized least squares to correct for both panel heteroskedasticity and temporally correlated errors. We argue that it is best to model dynamics via a lagged dependent variable rather than via serially correlated errors. The lagged dependent variable approach makes it easier for researchers to examine dynamics and allows for natural generalizations in a manner that the serially correlated errors approach does not. We also show that the generalized least squares correction for panel heteroskedasticity is, in general, no improvement over ordinary least squares and is, in the presence of parameter heterogeneity, inferior to it. In the conclusion we present a unified method for analyzing time-series-cross-section data.

scholarly journals PARAMETRIC ESTIMATION METHODS FOR BIVARIATE COPULA IN RAINFALL APPLICATION

2018 ◽  
Vol 81 (1) ◽  
Author(s):  
Rahmah Mohd Lokoman ◽  
Fadhilah Yusof
Keyword(s):  
Empirical Study ◽  
Sample Size ◽  
Small Sample Size ◽  
Empirical Studies ◽  
Daily Rainfall ◽  
Small Sample ◽  
Parametric Estimation ◽  
Estimation Methods ◽  
Dependence Structure ◽  
Correlation Level

This study focuses on the parametric methods: maximum likelihood (ML), inference function of margins (IFM), and adaptive maximization by parts (AMBP) in estimating copula dependence parameter. Their performance is compared through simulation and empirical studies. For empirical study, 44 years of daily rainfall data of Station Kuala Krai and Station Ulu Sekor are used. The correlation of the two stations is statistically significant at 0.4137. The results from the simulation study show that when the sample size is small (n <1000) for correlation level less than 0.80, IFM has the best performance. While, when the sample size is large (n ≥ 1000) for any correlation level, AMBP has the best performance. The results from the empirical study also show that AMBP has the best performance when the sample size is large. Thus, in order to estimate a precise Copula dependence parameter, it can be concluded that for parametric approaches, IFM is preferred for small sample size and has correlation level less than 0.80 and AMBP is preferred for larger sample size and for any correlation level. The results obtained in this study highlight the importance of estimating the dependence structure of the hydrological data. By using the fitted copula, Malaysian Meteorological Department will able to generate hydrological events for a system performance analysis such as flood and drought control system.

scholarly journals Scale-Selective Ridge Regression for Multimodel Forecasting

2013 ◽  
Vol 26 (20) ◽  
pp. 7957-7965 ◽  
Author(s):  
Timothy DelSole ◽  
Liwei Jia ◽  
Michael K. Tippett
Keyword(s):  
Least Squares ◽  
Ridge Regression ◽  
Large Scale ◽  
Small Sample Size ◽  
Ordinary Least Squares ◽  
Small Sample ◽  
Spatial Gradients ◽  
Smoothness Constraint ◽  
Grid Points ◽  
The Individual

Abstract This paper proposes a new approach to linearly combining multimodel forecasts, called scale-selective ridge regression, which ensures that the weighting coefficients satisfy certain smoothness constraints. The smoothness constraint reflects the “prior assumption” that seasonally predictable patterns tend to be large scale. In the absence of a smoothness constraint, regression methods typically produce noisy weights and hence noisy predictions. Constraining the weights to be smooth ensures that the multimodel combination is no less smooth than the individual model forecasts. The proposed method is equivalent to minimizing a cost function comprising the familiar mean square error plus a “penalty function” that penalizes weights with large spatial gradients. The method reduces to pointwise ridge regression for a suitable choice of constraint. The method is tested using the Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) hindcast dataset during 1960–2005. The cross-validated skill of the proposed forecast method is shown to be larger than the skill of either ordinary least squares or pointwise ridge regression, although the significance of this difference is difficult to test owing to the small sample size. The model weights derived from the method are much smoother than those obtained from ordinary least squares or pointwise ridge regression. Interestingly, regressions in which the weights are completely independent of space give comparable overall skill. The scale-selective ridge is numerically more intensive than pointwise methods since the solution requires solving equations that couple all grid points together.

INVESTIGATING THE IMPACT OF MULTICOLLINEARITY ON LINEAR REGRESSION ESTIMATES.

2021 ◽  
Vol 6 (1) ◽  
pp. 698
Author(s):  
Kunle Bayo Adewoye ◽  
Ayinla Bayo Rafiu ◽  
Titilope Funmilayo Aminu ◽  
Isaac Oluyemi Onikola
Keyword(s):  
Linear Regression ◽  
Sample Size ◽  
Least Squares ◽  
Ridge Regression ◽  
Research Work ◽  
Ordinary Least Squares ◽  
Small Sample ◽  
Elastic Net ◽  
Sample Sizes ◽  
The Impact

Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated. The aim of the study was to investigate the impact of multicollinearity on linear regression estimates. The study was guided by the following specific objectives, (i) to examined the asymptotic properties of estimators and (ii) to compared lasso, ridge, elastic net with ordinary least squares. The study employed Monte-carlo simulation to generate set of highly collinear and induced multicollinearity variables with sample sizes of 25, 50, 100, 150, 200, 250, 1000 as a source of data in this research work and the data was analyzed with lasso, ridge, elastic net and ordinary least squares using statistical package. The study findings revealed that absolute bias of ordinary least squares was consistent at all sample sizes as revealed by past researched on multicollinearity as well while lasso type estimators were fluctuate alternately. Also revealed that, mean square error of ridge regression was outperformed other estimators with minimum variance at small sample size and ordinary least squares was the best at large sample size. The study recommended that ols was asymptotically consistent at a specified sample sizes on this research work and ridge regression was efficient at small and moderate sample size.

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.

Application of Ultrasound Elastography for Assessing Intestinal Fibrosis in Inflammatory Bowel Disease: Fiction or Reality?

2020 ◽  
Vol 21 ◽  
Author(s):  
Roberto Gabbiadini ◽  
Eirini Zacharopoulou ◽  
Federica Furfaro ◽  
Vincenzo Craviotto ◽  
Alessandra Zilli ◽  
...  
Keyword(s):  
Inflammatory Bowel Disease ◽  
Sample Size ◽  
Bowel Disease ◽  
Small Sample Size ◽  
Shear Wave Elastography ◽  
Small Sample ◽  
Ultrasound Elastography ◽  
Invasive Technique ◽  
Intestinal Fibrosis ◽  
Inflammatory Bowel

Background: Intestinal fibrosis and subsequent strictures represent an important burden in inflammatory bowel disease (IBD). The detection and evaluation of the degree of fibrosis in stricturing Crohn’s disease (CD) is important to address the best therapeutic strategy (medical anti-inflammatory therapy, endoscopic dilation, surgery). Ultrasound elastography (USE) is a non-invasive technique that has been proposed in the field of IBD for evaluating intestinal stiffness as a biomarker of intestinal fibrosis. Objective: The aim of this review is to discuss the ability and current role of ultrasound elastography in the assessment of intestinal fibrosis. Results and Conclusion: Data on USE in IBD are provided by pilot and proof-of-concept studies with small sample size. The first type of USE investigated was strain elastography, while shear wave elastography has been introduced lately. Despite the heterogeneity of the methods of the studies, USE has been proven to be able to assess intestinal fibrosis in patients with stricturing CD. However, before introducing this technique in current practice, further studies with larger sample size and homogeneous parameters, testing reproducibility, and identification of validated cut-off values are needed.

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