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The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector

In statistical inference, estimation of spatial data parameters using the GWR approach has been carried out by many researchers. According to [

Harini and Purhadi [

Another problem that often arises in the GWR model is to validate hypothesis testing using statistical inference analysis because invalidating hypothesis test requires several stages of parameter estimation that cannot be done globally [

In this research, we focus on the form and properties of the estimated error variance-covariance parameters of the MGWR model using the MLE and WLS methods. This test uses statistical inference procedures to obtain the estimated error variance-covariance parameters that meet the unbiased nature.

Supporting theories for completing this research refer to the Geographically Weighted Regression (GWR) [

The MGWR method refers to [

The MGWR is the development of a multivariate linear model with known location information. In the multivariate spatial linear model, the relationship between the response variable

The assumptions used in the MGWR model are error vector

From Equation (

The vector error at the location

where

About the local character of the MGWR model (3), the sum of square error

If

To get the

where

and variance error is

Based on (8), then (6) can be described as follows:

From Equation (

Since

If the errors of estimated parameter variance-covariance MGWR model at the-

First, the variance-covariance error at the-

Furthermore,

where

If

From Equation (

To determine

and

Based on Propositions

If

Based on Proposition

and

By using the characteristics of the matrix

If

and in the same way, we obtain

where

By using Theorem

Since the variance-covariance error matrix

Thus, it is proven that if

This research concludes that the MGWR model using MLE and WLS methods is suitable to obtain the estimated error variance-covariance parameters. The results prove that

The authors declare that all of data is original and there is no data from others publication.

The authors declare that there is no conflict of interests regarding the publication of this article.

We would like to express our sincere gratitude to the Research Sub-Directorate, Community Development and Scientific Publications of the Directorate General of Islamic Higher Education (Dirjen DIKTIS) for providing funds for this research in 2018. Research and Community Service Institutions provide funding support with this publication.