2

2

5080

The Maximum Likelihood Method of Random Coefficient Dynamic Regression Model

The Random Coefficient Dynamic Regression (RCDR)
model is to developed from Random Coefficient Autoregressive
(RCA) model and Autoregressive (AR) model. The RCDR model
is considered by adding exogenous variables to RCA model. In this
paper, the concept of the Maximum Likelihood (ML) method is used
to estimate the parameter of RCDR(1,1) model. Simulation results
have shown the AIC and BIC criterion to compare the performance of
the the RCDR(1,1) model. The variables as the stationary and weakly
stationary data are good estimates where the exogenous variables
are weakly stationary. However, the model selection indicated that
variables are nonstationarity data based on the stationary data of the
exogenous variables.

Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.

1

10005322

An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Bayes method, Markov Chain Monte Carlo method,
Maximum Likelihood method, normal distribution.