Modified Inferential Methods on Restricted Parameters in Multivariate Regression Analysis: Applications in Socio Modified Inferential Methods on Restricted Parameters in Multivariate Regression Analysis: Applications in Socio-demographic Research Modified Inferential Methods on Restricted Parameters in Multivariate demographic Research

Abstract

Efficient and significant empirical estimate of the multivariate regression parameters will be helpful for the policymaker to make the right decisions about sophisticated interrelated issues in the dynamic world. Since the end of the twentieth century, statisticians are going forward to develop unique working methodology for estimating and testing restricted parameters. This study reviews existing methods and proposed modified maximum likelihood estimator (MMLE), modified multivariate 𝑡 statistic and modified joint confidence regions to get efficient estimates and test statistic for exact linear restricted parameters of multivariate regression with continuous responses. The proposed estimator is unbiased, consistent and relatively efficient than classical maximum likelihood estimator. Likelihood ratio test, modified Akaike information criterion are applied to select the related predictors of multivariate responses. We also proposed a modified maximum likelihood estimator for restricted parameters of multivariate regression with mixed responses and evaluate the performance of the proposed estimation method based on relative efficiency criterion. A Monte Carlo experiment is conducted to examine relative performance of the modified methods.

We also proposed a modified two parameter weighted estimator (MTPWE) to estimate the stochastic linear restricted parameters in multivariate regression analysis. The study has revealed theoretically and numerically that the proposed MTPWE is consistent based on mean square error criterion and relatively efficient than conventional multivariate least square (MLSE) and weighted mixed estimator (MMWME) in multivariate extension. Moreover, A Monte Carlo simulation experiment has done to ensure a comparison of the MTPWE to the MLSE and MMWME for different restricted parameters of the various levels of correlation and sample size.

The proposed inferential approach has been also applied to detect the numerical nexus among socio-demographic determinants, food expenditure and total monthly expenditure in “Haor” areas of Bangladesh by using Household Income Expenditure Survey (HIES) dataset 2016. The study reveals that logarithm form of total monthly expenditure and food expenditure as multivariate continuous responses are significantly related to total operating land, logarithm form of family size and total monthly income (𝑝 < 0.01) considering a restriction on the parameters at 5% level of significance. Based on the simulation study and empirical application, the performance of the modified inferential approach is deemed more realistic than the existing methodology.