Estimating and Enhancing Parameters for Linear Regression Model with Multivariate t-Distribution using PSO
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Abstract
Linear regression is one of the significant subjects which the researchers have been addressed in their researches. It is based on the assumption that random errors follow a normal distribution, traditional and Bayesian estimation. These methods were used for estimating parameters for linear regression model. Then, the two estimation methods can be compare based on measures (unbiasedness, mean square error) by analyzing real data if available, or using the simulation method to determine the appropriate method for estimation. As for this work, it focuses on the topic of parameters estimation with linear regression model when random errors have a multivariate t-distribution, using Maximum-Likelihood-Estimator (MLE) and Least-Square-Error (LSE) methods. Furthermore, the Particle- Swarm-Optimization (PSO) is useful for optimizing these methods by minimization these error methods. These methods are applied on real data (money supply and factors affected on it) for the years (2011-2021). The real data has been taken from Iraqi Central Bank. The Mean Square Error (MSE) result showed that a PSO method has less MSE as compared to two methods (MLE and LSE). The evidence to verify these MSE results evaluated in this research as the following: MLE=0.5949, Alternating Least Square approach (ALS)=0.20035, PSO=0.1859. PSO has also optimized the parameters of the linear regression model. It was concluded from MSE result findings that these results have become more accurate with PSO approach. The t-distribution is chosen because it used for small sample numbers or unknown variations.
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