A Discourse on Modified Likelihood Ratio (LR), Wald and Lagrange Multipliers (LM) Tests for Testing General Linear Hypothesis in Stochastic Linear Regression Model

C Narayana,B Mahaboob,J Ravi Sankar,P Balasiddamuni,B Venkateswarlu

doi:10.14419/ijet.v7i4.10.21222

C Narayana, B Mahaboob + Show 3 more

Open Access

https://doi.org/10.14419/ijet.v7i4.10.21222

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Abstract

In this research paper various new advanced inferential tools namely modified likelihood ratio (LR), Ward and Lagrange Multiplier test statistics have been proposed for testing general linear hypothesis in stochastic linear regression model. In this process internally studentized residuals have been used. This research study has brought out some new advance tools for analysing inferential aspects of stochastic linear regression models by using internally studentized residuals. Miguel Fonseca et.al [1] developed statistical inference in linear models dealing with the theory of maximum likelihood estimates and likelihood ratio tests under some linear inequality restrictions on the regression coefficients. Tim Coelli [2] used Monte carlo experimentation to investigate the finite sample properties of maximum likelihood (ML) and correct ordinary least squares (COLS) estimators of the half –normal stochastic frontier production function. In 2011, p. Bala siddamuni et.al [3] have developed advanced tools for mathematical and stochastic modelling.

Highlights

In spite of the availability of highly innovative tools in Mathematics, the main tool of the Applied Mathematician remains the stochastic regression model in the form of either linear or nonlinear model
Specification of the stochastic regression model is an important stage in any stochastic linear regression analysis
The various Misspecification tests and testing general linear hypothesis in the stochastic linear regression models were studied by many mathematicians and statisticians

Summary

Introduction

In spite of the availability of highly innovative tools in Mathematics, the main tool of the Applied Mathematician remains the stochastic regression model in the form of either linear or nonlinear model. Specification of the stochastic regression model is an important stage in any stochastic linear regression analysis. It includes specifying both the expectation function and the characteristics of the error. The various Misspecification tests and testing general linear hypothesis in the stochastic linear regression models were studied by many mathematicians and statisticians. Most of these people have proposed their tests in stochastic linear regression models by using some inferential criteria. Where R is a (mxk), (m

The multivariate probability density function of error vector is given by

Conclusion