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This paper shows the importance of the use of Monte Carlo experiments within Simple Linear Regression (SLR) Models through Refined Descriptive Sampling and proves practically that the asymptotic theory of the Ordinary Least Squares (OLS) estimator still hold with small samples when the Normality errors assumption is released. To this end, a simple Linear Regression adaptive Refined Descriptive Sampling (L2RDS) algorithm is proposed to estimate the parameter of SLR models by OLS method and computes its properties. Real data are used to properly specified the simulation model. The results show that L2RDS algorithm provides accurate and efficient point estimates. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariatet-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modified maximum likelihood estimation method that provides the estimator, called modified maximum likelihood estimator (MMLE), in closed form. These estimators are shown to be unbiased, efficient, and robust as compared to the widely used least square estimators (LSEs). Also, the tests based upon MMLEs are found to be more powerful than the similar tests based upon LSEs. [ABSTRACT FROM PUBLISHER]

Multiple linear regression models are frequently used in predicting unknown values of the response variabley. In this case, a regression model's ability to produce an adequate prediction equation is of prime importance. This paper discusses the predictive performance of ther-kandr-dclass estimators compared to ordinary least squares (OLS), principal components, ridge regression and Liu estimators and between each other. The theoretical results are illustrated using Portland cement data and a region is established where ther-kand ther-dclass estimators are uniformly superior to the other mentioned estimators. [ABSTRACT FROM AUTHOR]

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion. [ABSTRACT FROM PUBLISHER]