World Peace in the Light of Sīrah of the Prophet Muḥammad SAW

The advancement in science and technology has made the world peace and prosperity very important at this time in the human history. We find in the human history, since it was recorded, that almost all the civilizations were very intolerant, brutal to their opponents, especially, to the believers of other religions. On the other hand, the Islamic states were the most tolerant and accommodating to other religions. This fact is proved from the early history of Islām during the period of the Prophet Muḥammad (r) and his immediate successors. Similar is the case in the later history of the Muslims, during the period of the Abbasid, the Umayyids in Spain, the Turks, the Mughal era and in the Far East. Human and economic losses in wars were very huge during the first, the second world wars, and the current wars being fought in Iraq and Afghanistan. The human and material losses are horrible. The author believes that the Prophet Muḥammad (r) ’s teachings and traditions of moderation, tolerance, human respect, freedom of religious practice are the only ways to peace and prosperity in the world.

New Diagnostic Methods for Influential Observations in Linear Regression With Some Biased Estimation Methods

This thesis is concerned with the expansion of diagnostic methods in parametric regression models with some biased estimators. Of which, the Liu estimator, modified ridge estimator, improved Liu estimator and ridge estimator have been developed as an alternative to the ordinary least squares estimator in the presence of multicollinearity in linear regression models. Firstly, we introduce a type of Pena’s statistic for each point in Liu regression. Using the forecast change property, we simplify the Pena’s statistic in a numerical sense. It is found that the simplified Pena’s statistic behaves quite well as far as detection of influential observations is concerned. We express Pena’s statistic in terms of the Liu leverages and residuals. For numerical evaluation, simulated studies are given and a real data set has been analyzed for illustration. Secondly, we formulated Pena’s statistic for each point while considering the modified ridge regression estimator. Using this statistic, we showed that when modified ridge regression was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The normality of this statistic was also discussed and it was proved that it could detect a subset of high modified ridge leverage outliers. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. Next, we introduce a type of Pena’s statistic for each point in the improved Liu estimator. Using this statistic, we showed that when the improved Liu estimator was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration. The ridge estimator having growing and wider applications in statistical data analysis as an alternative technique to the ordinary least squares estimator to combat multicollinearity in linear regression models. In regression diagnostics, a large number of influence diagnostic methods based on numerous statistical tools have been discussed. Finally, we focus on ridge version of Nurunnabi et al. (2011) method for identification of multiple influential observation in linear regression. The efficiency of the proposed method is presented through several well-known data sets, an artificial large data with high-dimension and heterogeneous sample and a Monte Carlo simulation study.