Salah ud din AsgharSP16-RST-003LHR TP 5250Dr. Muhammad Noor-ul-amin2026-04-022018https://repository.cuilahore.edu.pk/handle/123456789/3163In the linear regression problems, ordinary least square (OLS) estimates violate in the presence of outliers as according to the assumptions of the OLS model that there should not be outliers in the data. More specifically, since the classical procedures are not applicable to the case of outliers presence. So, for the purpose of estimation there is another approach which handles this situation of outliers that is robust regression. Robust regression is an important tool for investigating data that are tainted with outliers and provide efficient results. In robust regression, estimates completely reject the effect of outliers and provide good estimates of the population parameter. In this work we focus on the problem of outliers occur in the data which provides a bad estimate of the population mean. In this dissertation, redescending M-estimator and ratio estimator have been proposed to estimate finite population mean using the information from auxiliary variable. Discussions have been made about the robust estimation method based on M-estimation, outliers, ratio estimators and auxiliary variable in Chapter 1. The literature about the robust regression and ratio estimator is discussed in Chapter 2. This research work is based on the two main chapters. The 3rd and 4th Chapters are the most important chapters of the thesis. For the first strategy, in the 3rd Chapter a redescending M-estimator is proposed by reworking on the redescending M-estimator proposed by Insha-ullah et al. (2006) which assign a weight closer to zero to the extreme values and closer to one to the good observations. Most of the redescending M-estimators are solved by iteratively reweighted least square method. For the second strategy we adopt the ratio estimators proposed by Kadilar and Cingi (2004) in the 4th Chapter and replace OLS coefficient with our redescending M-estimator proposed in 3rd Chapter in these ratio estimators. In both parts numerical illustrations and simulation studies were used to analyze the results of the proposed estimators with the comparative estimators to achieve the main results of the research. The intention of this research is to analyze, introduce and improve robust estimation methodologies to solve real life problems such as outliers in data. And finally in 5th chapter conclusion is written based upon whole the results of research.enDr. Muhammad Noor-ul-aminsp16Department of StatisticsSOCIAL SCIENCES::Statistics, computer and systems science::StatisticsRobust RegressionThesis