SOME PRACTICAL CONSIDERATIONS ABOUT PRECISION OF ESTIMATORS OF MINIMUM SQUARES AND LIKELIHOOD FOR THE PARAMETERS OF LINEAR REGRESSION NORMAL

Elisangela Aparecida da Silva Lizzi, Angela Achcar, Edson Zangiacomi Martinez, Jorge Achcar

Abstract


In this paper, we discuss some practical considerations on the use of different methods for the estimation of linear regression parameters and their impact on the obtained inferences. In practice, it is common to use some existing statistical software to obtain the least squares estimators (MSE) for the regression parameters and consider a non-biased estimator for the variance based on the residual squared sum of the residuals. Alternatively, we discuss the use of the maximum likelihood estimator (MLE) for the variance of the error (an unbiased estimator, but with smaller squared error) which may lead to different conclusions in terms of inferences. Two numerical examples are presented to illustrate the proposed method.


Keywords


Estimador de mínimos quadrados, Estimador de máxima verossimilhança, regressão linear, precisão

References


BICKEL P.J.; DOKSUM, K.A. Mathematical statistic: basic ideas and selected topics, vol 1, 2nd edn. Prentice Hall, Upper Saddle River, 2001

BOLFARINE,H.; SANDOVAL,H.E. Introdução à Inferência Estatística, ed. Sociedade Brasileira de Matemática, 2001

DRAPER, N.R.; SMITH, H. Applied regression analysis. Wiley series in probability and mathematical statistics, 1981.

MOOD, F.A.; GRAYBILL, D.C. Introduction to the Theory of Statistics. McGraw-Hill, 1974.

MONTGOMERY,D.C., PECK E.A. Introduction to Linear Regression Analysis, 2nd ed., John Wiley and Sons, Inc., New York, 1992.

MYERS,R.H. Classical and Modern Regression with Applications, 2th Ed., Duxbury Press, California USA, p.488,1990

NETER,J.; WASSERMAN, W.; KUTNER, M. H. Applied linear statistical models: regression, analysis of variance, and experimental designs, 2nd ed., Homewood, Ill. : R.D. Irwin,1985.

PANDOLFI, M.A.C. Implantação de estratégias tecnológicas e organizacionais em um ambiente em mudança: estudo de caso em uma empresa processadora de frutas tropicais, dissertação de mestrado profissional, Centro Universitário de Araraquara - UNIARA , 2013.

SEBER, G.A.F.; LEE, A.J. Linear regression analysis, second edition. Wiley series in probability and mathematical statistics, 2003.

WEISBERG,S Applied Linear Regression, 3ª Edição, John Wiley and Sons, Inc., New York, 2005




DOI: http://dx.doi.org/10.5902/2179460X17536

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