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.
