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۴۹۔ قید

قید

میں سانس تو لے رہا ہوں

مگر کسی کی اجارہ داری میں

یعنی !پر پھیلائے اڑ تو رہا ہوں

مگر گھر کی چار دیوری میں

تصوف کے غیر مشہور سلاسل کا تحقیقی جائزہ

Human being is the combination of two elements (body and soul). Soul is the eternal element in human being. Body of human is subordinate to disease and illness. Similarly soul can also get illness and inner disease. Human being visits doctors for cure and getting better physical health of body, likewise for the care and cure of the soul of human needs to have spiritual attachment, which is called tasawof. In Muslim society, it is believed that Tasawoof is confined to four categories (Salasil) i.e. Naqashbandiya, Chishtiya, Saharwardiya and Qadariya. In the same context it is also accepted that some other names of different salasil exist in different societies and books, which made the confusion in the  real picture and concept of Tasawof. This article is an attempt to find  these unfamiliar Salasil of tasawof and clarify their legal status. The researcher studied in this context which stated that tasawof is not restricted to the above mentioned four categories. The reason of less familiarization in the society is that the it was practiced by less followers at the time.

Influence Analysis of Some Alternatives to Ordinary Least Squares Estimator in Parametric Regression Models

This thesis investigates diagnostic methods in parametric regression models with some alternatives to ordinary least squares estimator. Of which, the Liu estimator has been developed as an alternative to the ordinary least squares estimator in the presence of collinearity among the regressors in linear regression models. Firstly, we presented the DFFITS and different versions of the Cook distance analogous to the ones given for the ordinary linear regression models of each individual observation on the Liu estimates. We suggested a version of the Cook distance based on one-step approximation. The mean shift outlier model for the Liu regression has also been investigated. Moreover, using the Sherman-Morrison-Woodbury theorem, we proposed approximate versions of the DFFITS and the Cook distance. Next, the pseudo likelihood function is given for estimating the regression coefficients and shape parameter as well as to establish local influence diagnostics. The normal curvatures of local influence are deduced under arbitrary perturbation schemes to detect influential observations. Then, we discussed the assessment of local influence under the modified ridge regression with normal error distribution. Using a pseudo-likelihood function, we expressed the normal curvatures of local influence for useful perturbation schemes in interpretable forms.Finally, local influence diagnostic methods in the modified ridge regression are deduced under heavy-tailed error distribution. The methods of analysis we presented have considerable significance for the detection of influential observations in the Liu and the modified ridge regression models. Examples using real-life data sets are used to illustrate the proposed methodology.
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