Main Article Content

Abstract

In a standard linear regression model the explanatory variables, , are considered to be fixed and hence assumed to be free from errors. But in reality, they are variables and consequently can be subjected to errors. In the regression literature there is a clear distinction between outlier in the - space or errors and the outlier in the X-space. The later one is popularly known as high leverage points. If the explanatory variables are subjected to gross error or any unusual pattern we call these observations as outliers in the - space or high leverage points. High leverage points often exert too much influence and consequently become responsible for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers etc. Although a good number of works has been done on the identification of high leverage points in linear regression model, this is still a new and unsolved problem in linear functional relationship model. In this paper, we suggest a procedure for the identification of high leverage points based on deletion of a group of observations. The usefulness of the proposed method for the detection of multiple high leverage points is studied by some well-known data set and Monte Carlo simulations.

Keywords

Errors in variable Leverages Masking Swamping Monte Carlo simulation

Article Details

Author Biographies

Abu Sayed Md. Al Mamun, University of Rajshahi

Associate Professor, Department of Satistiscs, 

Univesity of Rajshahi, Rajshahi-6205, Bangladesh.

A.H.M. R. Imon, Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA.


Professor, Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA.

A. G. Hussin, Faculty of Science and Defence Technology, National Defence University of Malaysia, Kuala Lumpur, Malaysia.


Professor, Faculty of Science and Defence Technology, National Defence University of Malaysia,
Kuala Lumpur, Malaysia.

Y. Z. Zubairi, Mathematics Division, Centre for Foundation Studies in Science, University of Malaya, Kuala Lumpur, Malaysia.

Associate Professor,Mathematics Division, Centre for Foundation Studies in Science, University of Malaya,
Kuala Lumpur, Malaysia.

Sohel Rana, Department of Applied Statistics, East West University, Dhaka, Bangladesh.

Associate Professor,Department of Applied Statistics, East West University, Dhaka, Bangladesh.
How to Cite
Md. Al Mamun, A. S., Imon, A. R., Hussin, A. G., Zubairi, Y. Z., & Rana, S. (2020). Identification of High Leverage Points in Linear Functional Relationship Model. Pakistan Journal of Statistics and Operation Research, 16(3), 491-500. https://doi.org/10.18187/pjsor.v16i3.2620

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