In the linear regression model, least-squares (LS) estimator is usually used for estimating regression parameters. LS is an unreliable and unfavourable estimator when multicollinearity and outlier problems exist in the model. Therefore, we propose a new robust regression estimator for solving the abovementioned problems simultaneously. We conducted theoretical comparisons and different scenarios of simulation studies, and a real-life dataset was employed to show the performance of the proposed estimator. Results showed that the proposed estimator performs better than other estimators when multicollinearity and outlier problems occur simultaneously in the model.

The beta regression model is commonly used when analyzing data that come in the form of rates or percentages. However, a problem that may encounter when analyzing these kinds of data that has not been investigated for this model is the multicollinearity problem. It is well known that the maximum likelihood (ML) method is very sensitive to high inter-correlation among the explanatory variables. Therefore, this paper proposes some ridge estimators for the beta regression model to remedy the problem of instability of the traditional ML method and increase the efficiency of estimation. The performance of ridge estimators is compared to the ML estimator through the mean squared error (MSE) and the mean absolute error (MAE) criteria by conducting a Monte-Carlo simulation study and through an empirical application. According to the simulation and application results, the proposed estimators outperform the ML estimator in terms of MSE and MAE.

The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood estimator (PMLE). There is a tendency that the explanatory variables grow together, which results in the problem of multicollinearity. The variance of the PMLE becomes inflated in the presence of multicollinearity. The Poisson ridge regression (PRRE) and Liu estimator (PLE) have been suggested as an alternative to the PMLE. However, in this study, we propose a new estimator to estimate the regression coefficients for the PRM when multicollinearity is a challenge. We perform a simulation study under different specifications to assess the performance of the new estimator and the existing ones. The performance was evaluated using the scalar mean square error criterion and the mean squared error prediction error. The aircraft damage data was adopted for the application study and the estimators’ performance judged by the SMSE and the mean squared prediction error. The theoretical comparison shows that the proposed estimator outperforms other estimators. This is further supported by the simulation study and the application result.

The novel coronavirus COVID-19 is spreading across the globe. By 30 Sep 2020, the World Health Organization (WHO) announced that the number of cases worldwide had reached 34 million with more than one million deaths. The Kingdom of Saudi Arabia (KSA) registered the first case of COVID-19 on 2 Mar 2020. Since then, the number of infections has been increasing gradually on a daily basis. On 20 Sep 2020, the KSA reported 334,605 cases, with 319,154 recoveries and 4,768 deaths. The KSA has taken several measures to control the spread of COVID-19, especially during the Umrah and Hajj events of 1441, including stopping Umrah and performing this year’s Hajj in reduced numbers from within the Kingdom, and imposing a curfew on the cities of the Kingdom from 23 Mar to 28 May 2020. In this article, two statistical models were used to measure the impact of the curfew on the spread of COVID-19 in KSA. The two models are Autoregressive Integrated Moving Average (ARIMA) model and Spatial Time-Autoregressive Integrated Moving Average (STARIMA) model. We used the data obtained from 31 May to 11 October 2020 to assess the model of STARIMA for the COVID-19 confirmation cases in (Makkah, Jeddah, and Taif) in KSA. The results show that STARIMA models are more reliable in forecasting future epidemics of COVID-19 than ARIMA models. We demonstrated the preference of STARIMA models over ARIMA models during the period in which the curfew was lifted.