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2021
Awwad, F. A., M. A. Mohamoud, and M. R. Abonazel, "Estimating COVID-19 cases in Makkah region of Saudi Arabia: Space-time ARIMA modeling", PLOS ONE, vol. 16, no. 4: Public Library of Science, pp. 1-16, 04, 2021. AbstractWebsite

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.

Rady, E. - H. A., M. R. Abonazel, and M. H. Metawe'e, "A Comparison Study of Goodness of Fit Tests of Logistic Regression in R: Simulation and Application to Breast Cancer Data", Academic Journal of Applied Mathematical Sciences, vol. 7, issue 1, pp. 50-59, 2021. Abstracta_comparison_study_of_goodness_of_fit_tests_of_logistic_regression_in_r.pdf

Goodness of fit (GOF) tests of logistic regression attempt to find out the suitability of the model to the data. The null hypothesis of all GOF tests is the model fit. R as a free software package has many GOF tests in different packages. A Monte Carlo simulation has been conducted to study two situations; the first, studying the ability of each test, under its default settings, to accept the null hypothesis when the model truly fitted. The second, studying the power of these tests
when assumptions of sufficient linear combination of the explanatory variables are violated (by omitting linear covariate
term, quadratic term, or interaction term). Moreover, checking whether the same test in different R packages had the
same results or not. As the sample size supposed to affect simulation results, so the pattern of change of GOF tests results under different sample sizes as well as different model settings was estimated. All tests accept the null hypothesis (more than 95% of simulation trials) when the model truly fitted except modified Hosmer-Lemeshow test in "LogisticDx" package under all different model settings and Osius and Rojek’s (OsRo) test when the true model had an interaction
term between binary and categorical covariates. In addition, le Cessie-van Houwelingen-Copas-Hosmer unweighted sum of squares (CHCH) test gave unexpected different results under different packages. Concerning the power study, all tests had a very low power when a departure of missing covariate existed. Generally, stukel's test (package 'LogisticDX) and CHCH test (package "RMS") reached a power in detecting a missing quadratic term greater than 80% under lower sample size while OsRo test (package 'LogisticDX') was better in detecting missing interaction term. Beside the simulation study, we evaluated the performance of GOF tests using the breast cancer dataset.

Awwad, F. A., B. J. Francis, and M. R. Abonazel, "Down syndrome, temporal variation and fallout radiation revisited: statistical evidence", Commun. Math. Biol. Neurosci., vol. 2021, pp. Article–ID, 2021. Abstract
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Farghali, R. A., M. Qasim, G. B. M. Kibria, and M. R. Abonazel, "Generalized two-parameter estimators in the multinomial logit regression model: methods, simulation and application", Communications in Statistics - Simulation and Computation: Taylor & Francis, pp. 1-16, 2021. AbstractWebsite

AbstractIn this article, we propose generalized two-parameter (GTP) estimators and an algorithm for the estimation of shrinkage parameters to combat multicollinearity in the multinomial logit regression model. In addition, the mean squared error properties of the estimators are derived. A simulation study is conducted to investigate the performance of proposed estimators for different sample sizes, degrees of multicollinearity, and the number of explanatory variables. Swedish football league dataset is analyzed to show the benefits of the GTP estimators over the traditional maximum likelihood estimator (MLE). The empirical results of this article revealed that GTP estimators have a smaller mean squared error than the MLE and can be recommended for practitioners.

Abonazel, M. R., F. A. Awwad, A. F. Lukman, I. B. Lekara-Bayo, E. Y. Atanu, and others, "Long-run determinants of Nigerian inflation rate: ARDL bounds testing approach", WSEAS Transactions on Business and Economics, vol. 18: WSEAS, pp. 1370–1379, 2021. Abstract
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Lukman, A. F., B. Aladeitan, K. Ayinde, and M. R. Abonazel, "Modified ridge-type for the Poisson regression model: simulation and application", Journal of Applied Statistics: Taylor & Francis, pp. 1-13, 2021. AbstractWebsite

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.

Abonazel, M. R., and O. Shalaby, "On Labor Productivity in OECD Countries: Panel Data Modeling", WSEAS TRANSACTIONS on BUSINESS and ECONOMICS, vol. 18, 2021. Abstract

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Abonazel, M. R., S. M. El-sayed, and O. M. Saber, "Performance of robust count regression estimators in the case of overdispersion, zero inflated, and outliers: simulation study and application to German health data", Commun. Math. Biol. Neurosci., vol. 2021, pp. Article–ID, 2021. Abstract
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Dawoud, I., and M. R. Abonazel, "Robust Dawoud–Kibria estimator for handling multicollinearity and outliers in the linear regression model", Journal of Statistical Computation and Simulation, vol. 91, no. 17: Taylor & Francis, pp. 3678–3692, 2021. Abstract
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Youssef, A. H., A. R. Kamel, and M. R. Abonazel, "Robust SURE estimates of profitability in the Egyptian insurance market", Statistical journal of the IAOS, vol. 37, no. 4: IOS Press, pp. 1275–1287, 2021. Abstract
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El-Masry, A. M., A. H. Youssef, and M. R. Abonazel, "Using logit panel data modeling to study important factors affecting delayed completion of adjuvant chemotherapy for breast cancer patients", Commun. Math. Biol. Neurosci., vol. 2021, pp. Article–ID, 2021. Abstract
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2020
Abonazel, M. R., and O. A. Shalaby, "Using Dynamic Panel Data Modeling to Study Net FDI Inflows in MENA Countries", Studies in Economics and EconometricsStudies in Economics and Econometrics, vol. 44, issue 2: Routledge, pp. 1 - 28, 2020. AbstractWebsite

Foreign direct investment (FDI) plays a critical role in providing financial capital needs, technology transfer, and creating more jobs in the host country. It also helps economies to increase competitiveness and productivity, thereby increasing exports and enhancing opportunities for growth and development. Middle East and North Africa (MENA) countries are in desperate need of more FDI inflows to resolve their economic problems. This paper investigates the determinants of net FDI inflows to 23 countries in MENA region during the period from 1995 to 2017 by using static and dynamic panel data analysis. The results indicate that macro determinants, such as gross domestic product (GDP) growth rate, openness, the inflation rate, and public expenditure have a significant impact on net FDI inflows. In addition, we observe that rents from natural resource (oil), exchange rate, and total reserves of foreign exchange and monetary gold do not significantly influence FDI.

Abonazel, M. R., and O. M. Saber, "A Comparative Study of Robust Estimators for Poisson Regression Model with Outliers", Journal of Statistics Applications and Probability, vol. 9, issue 2, pp. 279-286, 2020. Abstracta_comparative_study_of_robust_estimators_for_poisson.pdfWebsite

The present paper considers Poisson regression model in case of the dataset that contains outliers. The Monte Carlo simulation study was conducted to compare the robust (Mallows quasi-likelihood, weighted maximum likelihood) estimators with the nonrobust (maximum likelihood) estimator of this model with outliers. The simulation results showed that the robust estimators give better performance than maximum likelihood estimator, and the weighted maximum likelihood estimator is more efficient than Mallows quasi-likelihood estimator.

Youssef, A. H., M. R. Abonazel, and O. A. Shalaby, "Determinants of Per Capita Personal Income in U.S. States: Spatial Fixed Effects Panel Data Modeling", Journal of Advanced Research in Applied Mathematics and Statistics, vol. 5, issue 1, pp. 1-13, 2020. Abstractdeterminants__of__per__capita__personal__income.pdf

Over the last decades, the Per Capita Personal Income (PCPI) variable was a common measure of the effectiveness of economic development policy. Therefore, this paper is an attempt to investigate the determinants of personal income by using spatial panel data models for 48 U.S. states during the period from 2009 to 2017. We utilize the three following models: spatial autoregressive (SAR) model, Spatial Error (SEM) Model, and Spatial Autoregressive Combined (SAC) model, with individual (or spatial) fixe deffects according to three different known methods for constructing spatial weights matrices: binary contiguity, inverse distance, and Gaussian transformation spatial weights matrix. Additionally, we pay attention for direct and indirect effects estimates of the explanatory variables for SAR, SEM, and SAC models. The second objective of this paper is to show how to select the appropriate model to fit our data.
The results indicate that the three used spatial weights matrices provide the same result based on goodness of fit criteria, and the SAC model is the most appropriate model among the models presented. However, the SAC model with spatial weights matrix based on inverse distance is better compared to other used models. Also, the results indicate that percentage of individuals with graduate or professional degree, real Gross Domestic Product (GDP) per capita,and number of nonfarm jobs have a positive impact on the PCPI, while the percentage of individuals without degree or bachelor’s degree have a negative impact on the PCPI.

Youssef, A. H., M. R. Abonazel, and E. G. Ahmed, "Estimating the Number of Patents in the World Using Count Panel Data Models", Asian Journal of Probability and Statistics, vol. 6, issue 4, pp. 24-33, 2020. Abstractestimating_the_number_of_patents_in_the_world_using_count_panel_data.pdfWebsite

In this paper, we review some estimators of count regression (Poisson and negative binomial) models in panel data modeling. These estimators based on the type of the panel data model (the model with fixed or random effects). Moreover, we study and compare the performance of these estimators based on a real dataset application. In our application, we study the effect of some economic variables on the number of patents for seventeen high-income countries in the world over the period from 2005 to 2016. The results indicate that the negative binomial model with fixed effects is the better and suitable for data, and the important (statistically significant) variables that effect on the number of patents in high-income countries are research and development (R&D) expenditures and gross domestic product (GDP) per capita.

Abonazel, M. R., "Handling Outliers and Missing Data in Regression Models Using R: Simulation Examples", Academic Journal of Applied Mathematical Sciences, vol. 6, issue 8, pp. 187-203, 2020. AbstractHandling outliers and missing data using R simulation examples.pdfWebsite

This paper has reviewed two important problems in regression analysis (outliers and missing data), as well as some handling methods for these problems. Moreover, two applications have been introduced to understand and study these
methods by R-codes. Practical evidence was provided to researchers to deal with those problems in regression modeling
with R. Finally, we created a Monte Carlo simulation study to compare different handling methods of missing data in the
regression model. Simulation results indicate that, under our simulation factors, the k-nearest neighbors method is the
best method to estimate the missing values in regression models.

Abonazel, M. R., and A. A. - E. Gad, "Robust partial residuals estimation in semiparametric partially linear model", Communications in Statistics - Simulation and Computation, vol. 49, issue 5: Taylor & Francis, pp. 1223-1236, 2020. AbstractWebsite

This paper presents a robust version of partial residuals technique to estimate parametric and nonparametric components in semiparametric partially linear model. The robust estimation of the parametric component is constructed by using an M-estimation after eliminating the effect of the nonparametric component on both the response and covariates based on the pseudo data. Finally, the nonparametric component is estimated robustly by using the residuals from the obtained M-estimation of the parametric component. Simulation studies and a real data analysis illustrate that the proposed estimator performs better than the existing estimations when outliers in the dataset or errors with heavy tails.

Abonazel, M., and N. Elnabawy, "Using the ARDL bound testing approach to study the inflation rate in Egypt", Economic consultant, vol. 31, issue 3, pp. 24-41, 2020. AbstractUsing the ARDL bound testing approach to study the inflation rate in Egypt

According to economic theory, the change in any economic variables may affect another economic variable through the time and these changes are not instantaneously, but also over future periods. The autoregressive distributed lag (ARDL) model has been used for decades to study the relationship between variables using a single equation time series. The ARDL model is one of the most general dynamic unrestricted models in econometric literature. In this model, the dependent variable is expressed by the lag and current values of independent variables and its own lag value.
This paper studies the dynamic causal relationships between inflation rate, foreign exchange rate, money supply, and gross domestic product (GDP) in Egypt during the period 2005: Q1 to 2018: Q2. Using the bounds testing approach to cointegration and error correction model, developed within an ARDL model, we investigate whether a long-run equilibrium relationship exists between the inflation rate and three determinants (foreign exchange rate, money supply, and GDP). The results indicate that the exchange rate and the growth in money supply have significant effects on the inflation rate in Egypt, while the real GDP has no significance effect on the inflation rate.

2019
Abonazel, M. R., and R. A. Farghali, "Liu-Type Multinomial Logistic Estimator", Sankhya B, vol. 81, issue 2, pp. 203-225, Sep, 2019. AbstractWebsite

Multicollinearity in multinomial logistic regression affects negatively on the variance of the maximum likelihood estimator. That leads to inflated confidence intervals and theoretically important variables become insignificant in testing hypotheses. In this paper, Liu-type estimator is proposed that has smaller total mean squared error than the maximum likelihood estimator. The proposed estimator is a general estimator which includes other biased estimators such as Liu estimator and ridge estimator as special cases. Simulation studies and an application are given to evaluate the performance of our estimator. The results indicate that the proposed estimator is more efficient and reliable than the conventional estimators.

Abonazel, M. R., "Advanced Statistical Techniques Using R: Outliers and Missing Data", Annual Conference on Statistics, Computer Sciences and Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, 2019. AbstractAdvanced_statistical_techniques_using_r_outliers_and_missing_data.pdf

This paper has reviewed two important problems in regression analysis (outliers and missing data), as well as some handling methods for these problems using R. Moreover, two R-applications have been introduced to understand these methods by R-codes. Finally, we created a simple simulation study to compare different handling methods of missing data; this is an example of how to create R-codes to perform Monte Carlo simulation studies.

El-sayed, S. M., M. R. Abonazel, and M. M. Seliem, "B-spline Speckman Estimator of Partially Linear Model", International Journal of Systems Science and Applied Mathematics, vol. 4, issue 4, pp. 53-59, 2019. Abstractb-spline_speckman_estimator_of_partially_linear_model.pdf

The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for this model; where the main difference between these estimators is the estimation method used to estimate the nonparametric component, since the parametric component is estimated by least squares method mostly. The Speckman estimator is one of the commonly used for estimating the parameters of the PLM, this estimator based on kernel smoothing approach to estimate nonparametric component in the model. According to the papers in nonparametric regression, in general, the spline smoothing approach is more efficient than kernel smoothing approach. Therefore, we suggested, in this paper, using the basis spline (B-spline) smoothing approach to estimate nonparametric component in the model instead of the kernel smoothing approach. To study the performance of the new estimator and compare it with other estimators, we conducted a Monte Carlo simulation study. The results of our simulation study confirmed that the proposed estimator was the best, because it has the lowest mean squared error.

Abonazel, M. R., and A. I. Abd-Elftah, "Forecasting Egyptian GDP Using ARIMA Models", Reports on Economics and Finance, vol. 5, issue 1, pp. 35 - 47, 2019. Abstractforecasting_egyptian_gdp_using_arima_models.pdf

The Gross Domestic Product (GDP) is that the value of all products and services made at intervals the borders of a nation in an exceedingly year. In this paper, the Box-Jenkins approach has been used to build the appropriate Autoregressive-Integrated Moving-Average (ARIMA) model for the Egyptian GDP data. Egypt’s annual GDP data obtained from the World-Bank for the years 1965 to 2016. We find that the appropriate statistical model for Egyptian GDP is ARIMA (1, 2, 1). Finally, we used the fitted ARIMA model to forecast the GDP of Egypt for the next ten years.

Abonazel, M. R., "Generalized estimators of stationary random-coefficients panel data models: asymptotic and small sample properties", REVSTAT – Statistical Journal, vol. 17, issue 4, pp. 493–521, 2019. Abstractgeneralized_estimators_of_stationary.pdf

This article provides generalized estimators for the random-coefficients panel data (RCPD) model where the errors are cross-sectional heteroskedastic and contemporaneously correlated as well as with the first-order autocorrelation of the time series errors. Of course, under the new assumptions of the error, the conventional estimators are not suitable for RCPD model. Therefore, the suitable estimator for this model and other alternative estimators have been provided and examined in this article. Furthermore, the efficiency comparisons for these estimators have been carried out in small samples and also we examine the asymptotic distributions of them. The Monte Carlo simulation study indicates that the new estimators are more efficient than the conventional estimators, especially in small samples.

Abonazel, M. R., "New Ridge Estimators of SUR Model When the Errors are Serially Correlated", International Journal of Mathematical Archive, vol. 10, issue 7, pp. 53-62, 2019. Abstractnew_ridge_estimators.pdf

This paper considers the seemingly unrelated regressions (SUR) model when the errors are first-order serially correlated as well as the explanatory variables are highly correlated. We proposed new ridge estimators for this model under these conditions. Moreover, the performance of the classical (Zellner’s and Parks’) estimators and the proposed (ridge) estimators has been examined by a Monte Carlo simulation study. The results indicated that the proposed estimators are efficient and reliable than the classical estimators.

Elgohary, M. M., M. R. Abonazel, N. M. Helmy, and A. R. Azazy, "New robust-ridge estimators for partially linear model", International Journal of Applied Mathematical Research, vol. 8, no. 2, pp. 46–52, 2019. Abstractnew_robust-ridge_estimators_for_partially_linear_model.pdf

This paper considers the partially linear model when the explanatory variables are highly correlated as well as the dataset contains outliers. We propose new robust biased estimators for this model under these conditions. The proposed estimators combine least trimmed squares and ridge estimations, based on the spline partial residuals technique. The performance of the proposed estimators and the Speckman-spline estimator has been examined by a Monte Carlo simulation study. The results indicated that the proposed estimators are more efficient and reliable than the Speckman-spline estimator.