Statistics
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Item Simultaneous equation estimation with first order auto correlated disturbances(2013-08) Ojo, Y. O.; Adepoju, A. A.The estimation of the parameters of simultaneous equation problem is usually affected by the existence of mutual correlation between pairs of random deviates, which is a violation of the assumption of no autocorrelation between the error terms. In practice the form of correlation between the pairs of random deviates is not known. This study therefore examined a two-equation model in which the correlation between the random deviates is assumed to follow a first-order Autoregressive [AR (1)] process. Data was simulated using Monte Carlo approach with varying sample sizes each replicated 1000 times. The behaviour of OLS, 2SLS, LIML and 3SLS were evaluated using Variance, Root Mean Square Error (RMSE) and Absolute Bias (AB). The absolute bias estimates decrease in most cases as the sample size increases. The variances obtained by all the estimators reduced consistently as the sample size increases. There was no clear pattern in the behaviour of the RMSE across sample sizes. The results for = 0.3 were better than when = 0.0 with respect to each criterion but retained the same pattern. This work established that when was different from zero, the estimators performed better, hence the choice of should be carefully made as this may significantly affect the performances of the estimatorsItem Estimators of linear regression model with autocorrelated error terms and prediction using correlated uniform regressors(2012-11) Ayinde, K.; Adedayo, D. A.; Adepoju, A. A.Performances of estimators of linear regression model with autocorrelated error term have been attributed to the nature and specification of the explanatory variables. The violation of assumption of the independence of the explanatory variables is not uncommon especially in business, economic and social sciences, leading to the development of many estimators. Moreover, prediction is one of the main essences of regression analysis. This work, therefore, attempts to examine the parameter estimates of the Ordinary Least Square estimator (OLS), Cochrane-Orcutt estimator (COR), Maximum Likelihood estimator (ML) and the estimators based on Principal Component analysis (PC) in prediction of linear regression model with autocorrelated error terms under the violations of assumption of independent regressors (multicollinearity) using Monte-Carlo experiment approach. With uniform variables as regressors, it further identifies the best estimator that can be used for prediction purpose by averaging the adjusted co-efficient of determination of each estimator over the number of trials. Results reveal that the performances of COR and ML estimators at each level of multicollinearity over the levels of autocorrelation are convex – like while that of the OLS and PC estimators are concave; and that as the level of multicollinearity increases, the estimators perform much better at all the levels of autocorrelation. Except when the sample size is small (n=10), the performances of the COR and ML estimators are generally best and asymptotically the same. When the sample size is small, the COR estimator is still best except when the autocorrelation level is low. At these instances, the PC estimator is either best or competes with the best estimator. Moreover, at low level of autocorrelation in all the sample sizes, the OLS estimator competes with the best estimator in all the levels of multicollinearityItem Ranking of simultaneous equation estimators to outliers from heavy-tailed quasi-uniform distribution(2012-11) Oseni, B.M.; Adepoju, A. A.; Olubusoye, O. E.In this work, the ranking of the performances of two-equation simultaneous models when outliers are presumed present in a convoluted exogenous variable is carried out. The exogenous variable is a convolution of normal and uniform distribution. Monte Carlo experiment was carried out to investigate the performances of four estimators namely: Ordinary Least Squares (OLS), Two Stage Least Squares (2SLS), Limited Information Maximum Likelihood (LIML) and Three Stage Least Squares (3SLS). Five sample sizes were used to allow for measure of asymptotic properties of these estimators. The experiment was replicated 1000 limes and the results were evaluated using Total Absolute Bias (TAB), Variance and Root Mean Squared Error (RMSE). It is observed that the performances of the estimators when lower triangular matrix is used are better than that of upper triangular matrix. OLS using TAB as evaluation criterion is better than the other estimators when an exogenous variable is convoluted for the just-identified equation. The performance of 2SLS is best for the over-identified equation. OLS possesses the least variance for both equations and both matrices while LIML has the worst variance in most crises. OLS possesses the smallest RMSE for both matrices and equations except with the over-identified equation using lower triangular matrix when an exogenous variable is convolutedItem Assessment of simultaneous equation techniques under the influence of outliers(2011) Oseni, B. M.; Adepoju, A. A.Most simultaneous equations estimation techniques are based on the assumptions of normality which gives little consideration to some atypical data often called outliers which may be present in the observations. The outliers may have some obvious distorting influence on the estimates produce by these techniques. This study investigates the distorting effect of outliers on four simultaneous equation estimation techniques through Monte Carlo method. Outliers of various degrees were introduced into observations of different sizes. The estimators were ranked based on their ability to absorb the shock due to outliers in the observations. The Total Absolute Bias (TAB), Variance and Root Mean Square Error (RMSE) were used in ranking the performances of the estimators. Based on the criterion of tab, two stages least squares (2SLS) ranked the best, closely followed by three stage least squares (3SLS) and ordinary least squares (OLS) in that order, while limited information maximum likelihood (LIML) was the poorest when outliers of not more than 5% are present in the observation. It is however, not strange to observe that OLS outperformed the other estimators when variance was used. This could be misleading since variance may be measured around a wrong parameter. Based on the criterion of RMSE, ordinary least squares yields estimates with the least value of RMSE while LIML yields the greatest when outliers of not more than 10% are present in the observation. Also it was established that OLS has the greatest capacity to absorb the shock due to the presence of outliers in the observation