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Articles by Arezoo Bagheri
Total Records ( 3 ) for Arezoo Bagheri
  Arezoo Bagheri and Mahsa Saadati
  Background: Sampling and estimating of hidden population sizes, such as injection drug users are important issues for health policy makers, because of exposing these populations to high risks diseases, such as HIV/AIDS. Materials and Methods: Respondent driven sampling is a successful method in terms of resulting in representative sample of hidden populations and finding unbiased estimates comparing to the other existing conventional methods. Results: The main purpose of this study is to define population proportion estimation of this sampling method for dichotomous and non-dichotomous variables. For non-dichotomous variables, reciprocal approach results in over-determination equations which can be solved by either least squares or data smoothing approaches, though the late one is much more effective. A hypothetical data has been employed to find the estimation of dichotomous and non-dichotomous variables for respondent driven sampling method. Conclusion: The novelty of data smoothing procedure to find respondent driven sampling estimates has been proved by this hypothetical data. Respondent driven sampling method could result in unbiased estimates of population proportions and it has been recommended to be applied for studying hidden population proportions.
  Arezoo Bagheri , Habshah Midi and A.H.M. Rahmatullah Imon
  Problem statement: High leverage points are extreme outliers in the X-direction. In regression analysis, the detection of these leverage points becomes important due to their arbitrary large effects on the estimations as well as multicollinearity problems. Mahalanobis Distance (MD) has been used as a diagnostic tool for identification of outliers in multivariate analysis where it finds the distance between normal and abnormal groups of the data. Since the computation of MD relies on non-robust classical estimations, the classical MD can hardly detect outliers accurately. As an alternative, Robust MD (RMD) methods such as Minimum Covariance Determinant (MCD) and Minimum Volume Ellipsoid (MVE) estimators had been used to identify the existence of high leverage points in the data set. However, these methods tended to swamp some low leverage points even though they can identify high leverage points correctly. Since, the detection of leverage points is one of the most important issues in regression analysis, it is imperative to introduce a novel detection method of high leverage points. Approach: In this study, we proposed a relatively new two-step method for detection of high leverage points by utilizing the RMD (MVE) and RMD (MCD) in the first step to identify the suspected outlier points. Then, in the second step the MD was used based on the mean and covariance of the clean data set. We called this method two-step Robust Diagnostic Mahalanobis Distance (RDMDTS) which could identify high leverage points correctly and also swamps less low leverage points. Results: The merit of the newly proposed method was investigated extensively by real data sets and Monte Carlo Simulations study. The results of this study indicated that, for small sample sizes, the best detection method is (RDMDTS) (MVE)-mad while there was not much difference between (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad for large sample sizes. Conclusion/Recommendations: In order to swamp less low leverage as high leverage point, the proposed robust diagnostic methods, (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad were recommended.
  Arezoo Bagheri and Habshah Midi
  Problem statement: The Least Squares (LS) method has been the most popular technique for estimating the parameters of a model due to its optimal properties and ease of computation. LS estimated regression may be seriously disturbed by multicollinearity which is a near linear dependency between two or more explanatory variables in the regression models. Even though LS estimates are unbiased in the presence of multicollinearity, they will be imprecise with inflated standard errors of the estimated regression coefficients. It is now evident that the multiple high leverage points which are the outliers in the X-direction may be the prime source of collinearity-influential observations. Approach: In this study, we had proposed robust procedures for the estimation of regression parameters in the presence of multiple high leverage points which cause multicollinearity problems. This procedure utilized mainly a one step reweighted least square where the initial weight functions were determined by the Diagnostic-Robust Generalized Potentials (DRGP). Here, we had incorporated the DRGP with different types of robust methods to downweight the multiple high leverage points which lead to reducing the effects of multicollinearity. The new proposed methods were called GM-DRGP-L1, GM-DRGP-LTS, M-DRGP, MM-DRGP, DRGP-MM. Some indicators had been defined to obtain the best performance robust method among the existing and new introduced methods. Results: The empirical study indicated that the DRGP-MM emerge to be more efficient and more reliable than other methods, followed by the GM-DRGP-LTS as they were able to reduce the most effect of multicollinearity. The results seemed to suggest that the DRGP-MM and the GM-DRGP-LTS offers a substantial improvement over other methods for correcting the problems of high leverage points enhancing multicollinearity. Conclusion/Recommendations: In order to solve the multicollinearity problems which are mainly due to the multiple high leverage points, two proposed robust methods, DRGP- MM and the GM-DRGP-LTS, were recommended.
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