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Youssef, A. H., and M. R. Abonazel, "Alternative GMM Estimators for First-order Autoregressive Panel Model: An Improving Efficiency Approach", Communications in Statistics - Simulation and Computation, vol. 46, issue 4, no. ja, pp. 3112-3128, 2017. AbstractWebsite

This paper considers first-order autoregressive panel model which is a
simple model for dynamic panel data (DPD) models. The generalized
method of moments (GMM) gives efficient estimators for these models.
This efficiency is affected by the choice of the weighting matrix which has
been used in GMM estimation. The non-optimal weighting matrices have
been used in the conventional GMM estimators. This led to a loss of
efficiency. Therefore, we present new GMM estimators based on optimal or
suboptimal weighting matrices. Monte Carlo study indicates that the bias
and efficiency of the new estimators are more reliable than the
conventional estimators.

Youssef, A. H., and M. R. Abonazel, "A Comparative Study for Estimation Parameters in Panel Data Model", InterStat Journal , vol. 2009, issue May,No. 2, pp. 1-17, 2009. Abstracta_comparative_study_for_estimation_parameters_in_panel_data_model__2009.pdfWebsite

This paper examines the panel data models when the regression coefficients are fixed, random, and mixed, and proposed the different estimators for this model. We used the Mote Carlo simulation for making comparisons between the behavior of several estimation methods, such as Random Coefficient Regression (RCR), Classical Pooling (CP), and Mean Group (MG) estimators, in the three cases for regression coefficients. The Monte Carlo simulation results suggest that the RCR estimators perform well in small samples if the coefficients are random. While CP estimators perform well in the case of fixed model only. But the MG estimators perform well if the coefficients are random or fixed.

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.

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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Youssef, A. H., A. A. El-sheikh, and M. R. Abonazel, "New GMM Estimators for Dynamic Panel Data Models", International Journal of Innovative Research in Science, Engineering and Technology, vol. 3, issue 10, pp. 16414-16425, 2014. Abstractnew_gmm_estimators_for_dynamic_panel_data_models.pdf

In dynamic panel data (DPD) models, the generalized method of moments (GMM) estimation gives efficient estimators. However, this efficiency is affected by the choice of the initial weighting matrix. In practice, the inverse of the moment matrix of the instruments has been used as an initial weighting matrix which led to a loss of efficiency. Therefore, we will present new GMM estimators based on optimal or suboptimal weighting matrices in GMM estimation. Monte Carlo study indicates that the potential efficiency gain by using these matrices. Moreover, the bias and efficiency of the new GMM estimators are more reliable than any other conventional GMM estimators.

Youssef, A. H., A. A. Elshekh, and M. R. Abonazel, "Improving the Efficiency of GMM Estimators for Dynamic Panel Models", Far East Journal of Theoretical Statistics, vol. 47, issue 2, pp. 171-189, 2014. Abstractimprove_the_efficiency_of_gmm_estimators_for_dynamic_panel_models.pdfWebsite

In dynamic panel models, the generalized method of moments (GMM) has been used in many applications since it gives efficient estimators. This efficiency is affected by the choice of the initial weighted matrix. It is common practice to use the inverse of the moment matrix of the instruments as an initial weighted matrix. However, an initial optimal weighted matrix is not known, especially in the system GMM estimation procedure. Therefore, we present the optimal weighted matrix for level GMM estimator, and suboptimal weighted matrices for system GMM estimator, and use these matrices to increase the efficiency of GMM estimator. By using the Kantorovich inequality (KI), we find that the potential efficiency gain becomes large when the variance of individual effects increases compared with the variance of the errors.

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.

R
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.

M
Mousa, A., A. H. Youssef, and M. R. Abonazel, "A Monte Carlo Study for Swamy’s Estimate of Random Coefficient Panel Data Model", InterStat Journal , vol. 2011, issue April, No. 4, pp. 1-12, 2011. Abstracta_monte_carlo_study_for_swamys_estimate_of_random_coefficient_panel_data_model_2011.pdfWebsite

A particularly useful approach for analyzing pooled cross sectional and time series data is Swamy's random coefficient panel data (RCPD) model. This paper examines the performance of Swamy's estimators and tests associated with this model by using Monte Carlo simulation. The Monte Carlo study shed some light into how well the Swamy's estimate perform in small, medium, and large samples, in cases when the regression coefficients are fixed, random, and mixed. The Monte Carlo simulation results suggest that the Swamy's estimate perform well in small samples if the coefficients are random and but it does not when regression coefficients are fixed or mixed. But if the samples sizes are medium or large, the Swamy's estimate performs well when the regression coefficients are fixed, random, or mixed.

L
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.

F
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.

E
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.

El-sheikh, A. A., M. R. Abonazel, and N. Gami, "A Review of Software Packages for Structural Equation Modeling: A Comparative Study", Applied Mathematics and Physics, vol. 5, issue 3, pp. 85-94, 2017. Abstracta_review_of_software_packages_for_structural_equation_modeling_a_comparative_study.pdf

Structural equation modeling (SEM) is a widely used statistical method in most of social science fields. Similar to other statistical methods, the choice of the appropriate estimation methods affects the results of the analysis, thus it was of importance to review some of SEM software packages and the availability of different estimation methods in these packages. Therefore, in this paper five SEM software packages (AMOS, LISREL, and three packages in R) dealing with SEM analysis were reviewed to guide the researcher about the usage of each package. Moreover, an empirical study was presented to assess the performance of different estimation methods under the existence of missing data. The results showed that full information maximum likelihood (FIML) was the best estimation method to deal with different missingness rates.

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.

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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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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A
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.

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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Abonazel, M. R., "Generalized Random Coefficient Estimators of Panel Data Models: Asymptotic and Small Sample Properties", American Journal of Applied Mathematics and Statistics, vol. 4, no. 2, pp. 46–58, 2016. AbstractWebsite

This paper provides a generalized model for the random-coefficients panel data 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, the conventional estimators, which used in standard random-coefficients panel data model, are not suitable for the generalized model. Therefore, the suitable estimator for this model and other alternative estimators have been provided and examined in this paper. Moreover, 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 reliable (more efficient) than the conventional estimators 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.

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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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., "Efficiency Comparisons of Different Estimators for Panel Data Models with Serially Correlated Errors: A Stochastic Parameter Regression Approach", International Journal of Systems Science and Applied Mathematics, vol. 3, no. 2: Science Publishing Group, pp. 37, 2018. Abstract
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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.