Parameter estimation in replicated linear functional relationship model in the presence of outliers

Authors

  • Azuraini Mohd Arif Universiti Malaya
  • Yong Zulina Zubairi Universiti Malaya
  • Abdul Ghapor Hussin Universiti Pertahanan Nasional Malaysia

DOI:

https://doi.org/10.11113/mjfas.v16n2.1633

Keywords:

Linear functional relationship model, outliers, replicated

Abstract

The relationship between two linear variables where both variables are observed with errors can be modeled using a linear functional relationship model. However, when there is no knowledge about the ratio of error variance, we proposed that one can use the replicated linear functional relationship model. The aim of this study is to compare the parameter estimates between unreplicated and replicated linear functional relationship model. The study also extends to examine the behavior of the estimators of the replicated linear functional relationship model in the presence of outliers. A simulation study is performed to investigate the performance of the model. In the absence of outlier, it is found that the value of the parameter estimates is almost similar for both models. Whereas in the presence of outliers, the parameter estimates of the replicated linear functional relationship model have a smaller mean square error as the number of observations increased. This suggests the superiority of the replicated model.

Author Biographies

Azuraini Mohd Arif, Universiti Malaya

Institute of Graduate Studies

Yong Zulina Zubairi, Universiti Malaya

Centre for Foundation Studies in Science

Abdul Ghapor Hussin, Universiti Pertahanan Nasional Malaysia

Faculty of Defence Science and Technology

References

Adcock, R. J. 1878. A problem in least squares. Annals of Mathematics. 5 (2): 53–54.

Al-Nasser, Amjad D., Ebrahem, M. A. 2005. A New nonparametric method for estimating the slope of simple linear measurement model in the presence of outliers. Pakistan Journal Statistics. 21 (3) 265–74.

Barnett, V. D. 1970. Fitting straight lines-the linear functional relationship with replicated observations. Applied Statistics. 19 (2): 135–44.

Buonaccorsi, J. P. 2010. Measurement Error Models, Methods and Applications. New York: Chapman and Hall. Fuller, Wayne A. 1987. Measurement Error Models. John Wiley & Sons.

Gencay, R., Gradojevic, N. 2011. Errors-in-variables estimation with

wavelets. Journal of Statistical Computation and Simulation. (81): 1545-1564.

Ghapor, A. A, Zubairi, Y. Z., Mamun, A. S. M. A., Imon, A. H. M. R. 2015. A robust nonparametric slope estimation in linear functional relationship model. Pakistan Journal Statistics. 31 (3):339-350

Goran, M. I., Driscoll, P., Johnson, R., Nagy, T. R., Hunter, G.. 1996. Cross-Calibration of Body-Composition Techniques against Dual-Energy X-Ray absorptiometry in young children. The American Journal of Clinical Nutrition. 63 (3): 299–305.

Hussin, A. G., Fieller, N., Stillman, E. 2005. Pseudo-replicates in the linear circular functional relationship model. Journal of Applied Sciences. 5: 138-143.

Kendall, M. G., Stuart, A. 1979. The Advanced Theory of Statistics.

London: Griffin. Vol. 2.

Kim, Geun, M. 2000. Outliers and Influential observations in the structural errors-in-variables model. Journal of Applied Statistics. 27 (4): 451–60.

Lindley, D.V. 1953. Estimation of a functional relationship. Biometrika. 40 (1/2): 47–49. Moran, P. A. P. 1971. Estimating structural and functional relationships. Journal of Multivariate Analysis. 1 (2): 232–55.

Neyman, J., Scott, E. L. 1951. On certain methods of estimating the linear structural relation. The Annals of Mathematical Statistics. 22 (3): 352–61.

Solari, Mary E. 1969. The ‘maximum Likelihood Solution’ of the Problem of Estimating a Linear Functional Relationship.” Journal of the Royal Statistical Society. Series B (Methodological). 31 (2): 372–75.

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Published

15-04-2020