In ridge regression analysis, the estimation of the ridge parameter k is an important problem. Many methods are available for estimating such a parameter. This article reviewed and proposed some estimators based on Kibria ( 2003 Kibria , B. M. G. ( 2003 ). Performance of some new ridge regression estimators . Communications in Statistics—Theory and Methods 32 : 419 – 435 . [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) and Khalaf and Shukur ( 2005 Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameters for regression problems . A34 : 1177 – 1182 . [Google Scholar] ). A simulation study has been made and mean squared error (MSE) criteria are used to compare the performances of the estimators. We observed that under certain conditions some of the proposed estimators performed well compared to the ordinary least squared (OLS) estimator and some existing popular estimators. Finally, a numerical example has been considered to illustrate the performance of the estimators.

The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques – at least when multicollinearity exist among the regressors.

The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised through Monte Carlo simulation. Finally, an empirical application is used to show the advantages of the proposed estimator.

The coronavirus outbreak is the most notable world crisis since the Second World War. The pandemic that originated from Wuhan, China in late 2019 has affected all the nations of the world and triggered a global economic crisis whose impact will be felt for years to come. This necessitates the need to monitor and predict COVID-19 prevalence for adequate control. The linear regression models are prominent tools in predicting the impact of certain factors on COVID-19 outbreak and taking the necessary measures to respond to this crisis. The data was extracted from the NCDC website and spanned from March 31, 2020 to May 29, 2020. In this study, we adopted the ordinary least squares estimator to measure the impact of travelling history and contacts on the spread of COVID-19 in Nigeria and made a prediction. The model was conducted before and after travel restriction was enforced by the Federal government of Nigeria. The fitted model fitted well to the dataset and was free of any violation based on the diagnostic checks conducted. The results show that the government made a right decision in enforcing travelling restriction because we observed that travelling history and contacts made increases the chances of people being infected with COVID-19 by 85% and 88% respectively. This prediction of COVID-19 shows that the government should ensure that most travelling agency should have better precautions and preparations in place before re-opening.