Page 41 - Special Topic Session (STS) - Volume 1

STS346 Abu Sayed M. et al.
correctly when there is 30% contamination. The performances of the newly
proposed all three rules, i.e., rules 3, 4 and 5 are very satisfactory. They have
almost 100% correct identification rate with very small swamping rates, if at
all.

4. Discussion and Conclusion
In this paper, our main objective was to propose a method of leverage
measures and then to develop an identification rule for the detection of high
leverage points in linear functional relationship model. After obtaining a
method of finding the fixed-X values, we propose three different identification
rules based on robust measures of leverages. Both numerical and simulation
results show that the traditionally used measures may often fail to identify
even a single high leverage point when 20% to 30% high leverage points are
present in the data. The 2M rule based on traditional leverage measure
possesses relatively very high swamping rate as well. However, the proposed
methods perform very well in every occasion. Our study clearly shows that they
can correctly identify all high leverage points without swamping low leverage
cases.

References
1. Abdullah, M. B. (1995). Detection of influential observations in functional
errors-in- variables model. Communications in Statistics: Theory and
Methods. 24:1585–1595.
2. Bagheri, A., Habshah, M. and Imon, A.H.M.R. (2009). Two-step robust
diagnostic method for identification of multiple high leverage points.
Journal of Mathematics and Statistics. 5: 97–206.
3. Chatterjee, S. and Hadi, A. S. (1988). Sensitivity Analysis in Linear Regression,
Wiley, New York.
4. Fuller, W.A. (1987). Measurement error models, Wiley, New York.
5. Habshah, M., Norazan, R. and Imon, A.H.M.R. (2009). The performance of
diagnostic-robust generalized potentials for the identification of multiple
high leverage points in linear regression. Journal of Applied Statistics. 36:
507–520.
6. Hadi, A.S. (1992). A new measure of overall potential influence in linear
regression. Computational Statistics and Data Analysis. 14: 1-27.
7. Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J. and Ostrowski, E. (1994)
A Handbook of Small Data Sets, Chapman and Hall, London.
8. Hoaglin, D.C. and Welsch, R.E. (1978). The hat matrix in regression and
ANOVA. The American Statistician. 32:17-22.
9. Hocking, R.R. and Pendleton, O.J. (1983). The regression dilemma.
Communications in Statistics-Theory and Methods. 12: 497-527.

30 | I S I W S C 2 0 1 9