On OLS Estimation of Stochastic Linear Regression Model
B. Mahaboob1, B.Venkateswarlu2, K.A. Azmath3, C. Narayana4, J. Peter Praveen5

1Dr B. Mahaboob, Department of Mathematics, Koneru Lakshmaiah Educational Foundation, Vaddeshwaram, Guntur, A.P., India.
2Dr B.Venkateswarlu, School of Advanced Science (SAS), Vellore Institute of Technology, Vellore, Tamil nadu , India.
3Dr K.A. Azmath, Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati, Andhra Pradesh.
4Dr C. Narayana, Mathematics Department, Sri Harsha institute of P.G Studies, Nellore Andhra Pradesh, India.
5J.Peter Praveen, Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, India.
Manuscript received on July 20, 2019. | Revised Manuscript received on August 10, 2019. | Manuscript published on August 30, 2019. | PP: 1953-1955| Volume-8 Issue-6, August 2019. | Retrieval Number: F7930088619/2019©BEIESP| DOI: 10.35940/ijeat.F7930.088619
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Abstract: This paper mainly discusses the formulation of stochastic linear statistical model and its assumptions and finally explores an important aspect namely the Ordinary Least Squares (OLS) estimation of stochastic linear regression model. In addition to these inference in stochastic linear regression model is also presented here. Nimitozbay et.al [1], in their paper proposed the weighted mixed regression estimation of the coefficient vector in a linear regression model with stochastic linear restrictions binding the regression coefficients. In 1980, P.A.V.B. Swamy et.al proposed a linear regression model where the coefficient vector is a weekly stationary multivariate stochastic process and that model provides a convenient representation of a general class of non-stationary processes. They proposed prediction and estimation methods which are linear and easy to compute. Daojiang et.al [2] in 2014, in their paper depicted an innovative estimation technique to the multicollinearity in statistical model which is linear in the case of existence of stochastic linear constraints on the parameters and a very different estimation technique was presented by mixing the OME and PCR estimator also known as SRPC regression estimator. In 2014, Shuling Wang et.al [3] in their paper proposed some diagnostic methods in restricted stochastic statistical models which are linear. Gil Gonjalez et.al [4], in 2007, in their paper, derived the LSEs for the simple linear statistical model and examined them from a theoretical perspective.
Keywords: Regression coefficient, Data matrix, error vector, Homoscedasticity, OLS estimator, t-test statistic. OME( Ordinary Mixed Estimator),PCR(Principal Components Regressor), SRPC (Stochastic Restricted Principal Components),LSE(Least Square Estimator).