Bello A Rasheed

Common problems in multiple linear regression models are multicollinearity and outliers. In this paper, we will propose a robust ridge regression. It is based on weighted ridge least trimmed squares (WRLTS). The proposed method (WRLTS) has been compared to some different estimation methods, namely the Ordinary Least Squares (OLS), Ridge Regression (RR),Robust Ridge Regression (RRR) such as Ridge LeastMedian Squares (RLMS), Ridge Least Trimmed Squares (RLTS) regression based on LTS estimator and Weighted Ridge (WRID) with respect to Standard Error. Two examples are used to illustrate the proposed method. In both examples, WRLTS is found to be the best estimator among the other methods in this paper.

This paper investigates the use of robust wild bootstrap techniques on regression model as an estimator for economic indicators in a situation where heteroscedasticity and outliers are present. We introduced robust procedures, called robust weighted bootstrap least trimmed squares (RWBootWu) and robust weighted bootstrap least trimmed squares (RWBootLiu). The propose method uses the weighted residuals incorporating the Huber weighted function, least trimmed squares (LTS) estimator, bootstrap sampling procedure of Wu and Liu as well as the robust location and scale,. Numerical examples and simulation were carried out to evaluate the performance of the RWBootWu and RWBootLiu with the existing wild bootstrap BootWu, BootLiu, RBootWu, and RBootLiu method. The result of the study proved that the (RWBootWu) and (RWBootLiu) offer as a substantial improvement over the existing methods and proved to be good alternative estimators.

Correlated survival data with possible censoring are frequently encountered in survival analysis.When there are dependencies among observed survival times, conventional Cox proportionalhazards model (CPHM) and Accelerated Failure Time (AFT) models that assumes independentresponses may not be appropriate. In this study, we compare the performance of parametric andsemi-parametric survival models with application to clinical data. Specifically, the AFT modeland the CPHM with and without Random effect were compared. Data on hypertension wascollected from Federal Medical Centre Keffi and General Hospital Nasarawa for the period offive years (2016 – 2020). The results from the analysis revealed that the Weibull AFT modelwith Gamma Random effect distribution had the least AIC and BIC values indicating that itoutperformed the other models considered in this study. Hence, the interpretation of the resultswas based on the most efficient model. Based on our results, it was found that hypertens...

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affecte...