Institute of Economics Research, Hitotsubashi University, Tokyo, Japan. Department of Population Science and Human Resource Development, University of Rajshahi, Bangladesh.
khan75ru@gmail.com
Study Area: Regression Diagnostics, Robust Statistics, Financial Econometrics, Time Series Analysis.
Abstract: In fitting a linear regression model by the least squares method, leverage values play a very important role. They often form the basis of regression diagnostics as measures of influential observations in the explanatory variables. Much work has been done on the detection of high leverage values and a good number of diagnostic measures are now available in the literature. In this paper, a comparative study on the detection of high leverage points is reported which includes most of the commonly used and recent diagnostic measures. The usefulness and/or limitations of different types of measures under a variety of leverage structures are studied through Monte Carlo simulation experiments.
Abstract: Leverage values are being used in regression diagnostics as measures of influential observations in the X-space. A good number of diagnostic techniques is now being used for the detection of high leverage points. It is therefore important to investigate the performances of different diagnostics. In this type of investigation Monte Carlo simulation study could be very useful since here we clearly know the real situation. It is a common practice over the years to consider the mean (average) of the simulated results as the central value of the required result. In this paper we show that considering mean as the central value could produce confusing results when the identification of high leverage points is concerned. We also investigate the performance of two other commonly used measures, the median and the trimmed mean as Monte Carlo simulated mean in the identification of high leverage points under a variety of leverage structures.
Abstract: In fitting a linear regression model by the least squares method, leverage values play a very important role. They often form the basis of regression diagnostics as measures of influential observations in the explanatory variables. Much work have been done on the detection of high leverage values and a good number of diagnostic measures are now available in the literature. But neither of these methods is effective in the identification of high leverage points when multiple high leverage points are present in the data. In our study we proposed a new method for the identification of multiple high leverage points. The usefulness of this newly proposed method is studied under a variety of leverage structures through Monte Carlo simulation experiments. We also investigated the performance of the newly proposed method as a remedy to multicollinearity problem caused by the presence of multiple high leverage points.
Abstract: In fitting a linear regression model by the least squares method, leverage values play a very important role. They often form the basis of regression diagnostics as measures of influential observations in the explanatory variables. Much work have been done on the detection of high leverage values and a good number of diagnostic measures are now available in the literature. In this paper, a comparative study on the detection of high leverage points is reported which includes most of the commonly used and recent diagnostic measures. The usefulness and/or limitations of different types of measures under a variety of leverage structures are studied through Monte Carlo simulation experiments.
