http://196.220.128.81:8080/xmlui/handle/123456789/232 Mon, 27 Apr 2026 05:35:23 GMT 2026-04-27T05:35:23Z http://196.220.128.81:8080/xmlui/handle/123456789/5591 A MONTE CARLO STUDY OF ALKHAMISI RIDGE ESTIMATOR AKINTOLA, OLUSESAN TOLULOPE In classical linear regression model, the existence of high correlations between two or more exogenous variables results to multicollinearity problem. This problem influences the ordinary least squares (OLS) estimator in producing inefficient estimates of the model parameters. Based on the aforementioned, application of ridge regression to obtain ridge parameter that will produce efficient estimates in the presence of multicollinearity becomes necessary. Several authors have studied modalities of setting ridge parameters that will give best estimates of the model parameters. This research work examined the ridge parameter estimation techniques of Alkhamisi ridge estimator, which has already been examined in different forms and in various types by some authors. However, the concept of various kinds of ridge estimators was introduced into the classification of Alkhamisi ridge parameter; this now resulted into proposing 228 new ridge parameters. The existing and proposed (228) ridge parameters were compared by conducting Monte Carlo simulation experiment 1000 times on a linear regression model with three (3) predictor variables (p=3), taking 𝛽0 = 0, 𝛽1 = 0.8, 𝛽2 = 0.1, 𝛽3 = 0.6. and seven (7) predictor variables (p=7), taking 𝛽0 = 0, 𝛽1 = 0.4, 𝛽2 = 0.1, 𝛽3 = 0.6, 𝛽4 = 0.2, 𝛽5 = 0.25, 𝛽6 = 0.3, 𝛽7 = 0.53, that exhibited different degrees of multicollinearity (ρ = 0.8, 0.9, 0.95, 0.99, 0.999, 0.9999), error variance (σ2 = 0.25, 1, 25) and six levels of sample size(n = 20, 30, 50, 100, 150, 250). At p=3, the problem of multicollinearity existed which was pronounced and corrected at p=7. In order to identify the proposed ridge estimators with most efficient estimates, their performances were compared with the existing results via mean square error criterion (MSE). From the results, it was noticed that the proposed estimators were among those that provided efficient estimates; some of them also performed better than the existing ones even after applying to simulated and real-life data. The best ridge parameter is K4FM1R. M.TECH THESIS Wed, 01 Sep 2021 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5591 2021-09-01T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5588 SOLVING HETEROSCEDASTICITY WITH MODIFIED BAYESIAN ADDITIVE REGRESSION TREES ADULOJU, OLUWATOBI MICHAEL Heteroscedasticity is often neglected during the analysis of high dimensional data but can pose a problem when using modern regression methods such as Bayesian Additive Regression Trees (BART), Random Forest, and Neural Networks. When predictors are more than the sample size, the BART model was computationally expensive and tedious; this prompted the development of the Bayesian Additive Regression Trees using Bayesian Modelling Average (BART-BMA) as an alternative. However, none of these methods are effective when heteroscedasticity is present in the data. We solved this challenge by modeling the variance component of the BART-BMA using multiplicative trees called the Modified Bayesian Additive Regression Trees (MBART). Heteroscedasticity was introduced into the data structure used by Friedman in 1991. The model's effectiveness was tested by applying the method to out-of-sample data, five-fold cross-validation, and a real-life dataset obtained from the University of California Machine Learning Cloud Storage, at different levels of sample sizes, trees, and predictor variables. The results indicated that MBART performed better than Random Forest, BART, and BART-BMA when applied to simulated out-of-sample data, the real-life data, and fivefold cross-validation at the levels of sample sizes 50, 100, and 500 and tree sizes (5, 10, 25, and 50). M.TECH.THESIS Mon, 01 Mar 2021 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5588 2021-03-01T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5587 SPATIAL ANALYSIS OF WOMEN’S EMPOWERMENT IN NIGERIA: AN ORDINAL REGRESSION APPROACH ADEYEMI, ESTHER IBUKUN There is a fast rising acknowledgement that women’s empowerment is essential to realising development goals, which would support economic growth, improvement in maternal and child health in interrelated development goals that are sustainable. A study into the geographical vari ability of women empowerment in Nigeria was investigated using the data set from 2018 Nigeria Demographic and Health Survey (NDHS). We looked into six separate indicators: Self esteem, contraceptive use, healthcare, access to media, decision making, occupation and earnings, using latent scores and factor analysis. Overall empowerment was constructed and a multinomial with ordered categories (Probit link) with geoadditive predictors was used in estimating the effects of demographic and geographical factors on the effect of empowerment result. Using a Bayesian ap proach, spatial effects in BayesX were assigned using Markov random field prior, modelling fixed effects were assigned using non-informative diffuse priors, bayesian P-Spilnes second order random walk for the non linear smooth functions. Bayesian model diagnostic were carried out with de viance information criterion. The results showed that women’s empowerment was associated with educational level, access to newspapers, place of residence, wealth index and listening to radio. We also observed that age of the woman and age difference of the partner was an important predictor of women’s empowerment. This study helps to explain the importance of socio-demographic and economic variables to women’s empowerment. Furthermore, the spatial effects was used to cap ture the influence of unobserved geographical factors, which are significant to permit modeling of fundamental processes, that has effect on women empowerment , thereby contributing to the body of knowledge on women empowerment in Nigeria. M.TECH.THESIS Thu, 01 Dec 2022 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5587 2022-12-01T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5586 SENSITIVITY ANALYSIS OF PRIOR DISTRIBUTION ON BAYESIAN LINEAR REGRESSION MODEL ADEREKUN, ADENIKE RACHEL This research work focused on Bayesian Linear Regression using sensitivity analysis of prior distribution. A sensitivity analysis allows to examine the final model results, based on the original prior, in relation to result that would be obtain using different priors. Perhaps, the regression model is the workhorse of econometrics. In Bayesian Statistical inference, a prior probability distribution of an uncertain quantity is the probability distribution that expresses uncertainty about the quantity before the data are taken into account. The parameters of the prior distribution are called hyper- parameters that distinguish them from parameter of the model of the data. In this study, the researcher reviewed the growth of the economy of a country has been determined by the Gross Domestic Product (GDP) which is one of the indicators that boost the economy. However, some micro-economic variables have been known to influence the Gross Domestic Product. In this research, the Gross Domestic Product per capital of Nigeria from 1989 to 2019 was studied as a function of money supply, foreign direct investment, unemployment and non-oil export. The ordinary least squares estimator and Bayesian approach were adopted to estimate the coefficients of the model. Normal, Gamma, Jeffrey and Uniform priors were considered. The Bayesian estimator with normal prior produced the most efficient estimator of the model coefficients. Prior sensitivity test was carried out and it is discovered that the Bayesian estimator with Jeffrey prior is less sensitive to change in hyper parameters. M.TECH. THESIS Sun, 01 Aug 2021 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5586 2021-08-01T00:00:00Z