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SPATIAL AUTOREGRESSIVE (SAR) MODEL WITH ENSEMBLE LEARNING-MULTIPLICATIVE NOISE WITH LOGNORMAL DISTRIBUTION (CASE ON POVERTY DATA IN EAST JAVA)

*Dewi Retno Sari Saputro orcid scopus  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Sulistyaningsih Sulistyaningsih  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Purnami Widyaningsih  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Open Access Copyright (c) 2021 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
The regression model that can be used to model spatial data is Spatial Autoregressive (SAR) model. The level of accuracy of the estimated parameters of the SAR model can be improved, especially to provide better results and can reduce the error rate by resampling method. Resampling is done by adding noise (noise) to the data using Ensemble Learning (EL) with multiplicative noise. The research objective is to estimate the parameters of the SAR model using EL with multiplicative noise. In this research was also applied a spatial regression model of the ensemble non-hybrid multiplicative noise which has a lognormal distribution of cases on poverty data in East Java in 2016. The results showed that the estimated value of the non-hybrid spatial ensemble spatial regression model with multiplicative noise with a lognormal distribution was obtained from the average parameter estimation of 10 Spatial Error Model (SEM) resulting from resampling. The multiplicative noise used is generated from lognormal distributions with an average of one and a standard deviation of 0.433. The Root Mean Squared Error (RMSE) value generated by the non-hybrid spatial ensemble regression model with multiplicative noise with a lognormal distribution is 22.99.
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Keywords: Additive noise; Ensemble, parameter estimation; SAR Model

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