Browsing by Author "Isiaka Oloyede"

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    Bayesian Generalized Least Squares with Autocorrelated Error
    (Journal of Statistical Modeling and Analytics, 2022) Isiaka Oloyede
    Autocorrelation plays a significant role in both time series and cross-sectional data. More often than none it rendered the inference of parameter estimates invalid and those other statistics that use the parameters. This study investigates the asymptotic behaviour of generalised least squares with Autocorrelated errors cum Markov Chain Monte Carlo simulation. Bias and Mean Squares Error criteria were used to evaluate the finite properties of the estimator. The following sample sizes: 25, 50, 100, and 250 were constructed and used. Thus 11,000 simulations with varying levels of Autocorrelated error were carried out. This is subjected to the level of convergence. Bias and Mean Squares Error criteria revealed improving performance asymptotically regardless of the level of Autocorrelated error. The study observed that asymptotic consistency and efficiency were obtained at the large sample which obeys the law of large number and points to the fact that variance of error terms tend towards zero and distribution tends to be normal when the law of large number is applied. In line with the above assertion, the study had developed novel Bayesian Generalized Least Squares Autocorrelated Estimator (BGLSAE) that capture the presence of autocorrelation in the dataset. The study, therefore recommended that large samples should be obtained to make the inferences stable.
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    Bayesian Hetero-Elasticnet (A Gibbs Sampler Approach)
    (Tanzania Journal of Science, 2021) Isiaka Oloyede
    Combined heteroscedasticity and multicollinearity as dual non-spherical disturbances were experimented asymptotically. A Gibbs Sampler technique was used to investigate the asymptotic properties of hetero-elasticnet estimator with mean squares error (MSE) and bias as performance metrics. The seed was set to 12345; β is set at β = {2.5,3,1.5,1,0,0,0.5}; Xs variables were generated as follow: the design matrix was generated from the multivariate normal distribution with mean > 0 and variance σi 2. X1 and X2 are truncated with Harvey (1976) heteroscedastic error structure; X3, … , X6 are collinear covariate with pairwise correlation between 0.6 and 0.9, the sample sizes were 25, 100 and 1000. The number of replications of the experiment was set at 10,000 with burn-in of 1000 which specified the draws that were discarded to remove the effects of the initial values. The thinning was set at 5 to ensure the removal of the effects of autocorrelation in the MCMC simulation. The study found that there is consistency of estimator asymptotically as the sample sizes increases from 25 to 50 so also to 1000, the larger sample size depicted least bias. The estimator exhibited efficiency asymptotically as larger sample sizes depicted least mean squares error. The study therefore recommended Bayesian hetero-elasticnet when data exhibit both heteroscedasticity and multicollinearity.
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    Bayesian Linear Restricted Least Squares Estimators
    (The Indian Society for Probability and Statistics, 2022) Isiaka Oloyede
    Bayesian Statistics had been outshined classical Statistics over the years due to its probabilistic approach to modelling and data analytics. In recent times, much of model complexity and data ambiguity emerged of which the existing methods have their drawbacks. Model complexity and data uncertainty most times exhibit multicollinearity which render the inferences of least squares invalid. This then call for improvement in the existing methods so as to capture the trend in model complexity and data uncertainty. The Monte Carlo simulations was adopted to compare the restricted least squares family of estimators (RLSFE) with the presence of multicollinearity and two sets of linear restrictions were imposed on the model. The risk values and relative efficiency of the RLSFE under quadratic loss function were estimated to compare the estimators. Bayesian restricted least squares estimator was derived, the posterior mean and Bayes estimate were deprioritised with prior mean. The study found out that posterior mean and Bayes estimates outperformed classical restricted least squares estimators due to their lower risk values. The relative efficiency pointed to the fact that posterior mean and Bayes estimates are most preferred and efficient. The study further observed monotonic increase in the risk values as the increases which proved the negative impact of multicollinearity of the inferences of regression parameters.