Robust Goodness of Fit Test Based on the Forward Search

Abbas Mahdavi^1,

¹Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

Cite this paper

Abbas Mahdavi. Robust Goodness of Fit Test Based on the Forward Search. American Journal of Applied Mathematics and Statistics. 2013; 1(1):6-10. doi: 10.12691/AJAMS-1-1-2

Abstract

The most frequency used goodness of fit tests are based on measuring the distance between the theoretical distribution function and the empirical distribution function (EDF), but presence of outliers influences these tests strongly. In this study, we propose a simple robust method for goodness of fit test by using the “Forward Search” (FS) method. The FS method is a powerful general method for identifying outliers and their effects on the hypothesized model. The performance and the ability of the procedure to capture the structure of data, even in the presence of outliers, are illustrated by some simulation studies and real data examples.

Keywords

forward search procedure, goodness of fit test, robust approach, outlier

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Hadi, A. S., Identifying multiple outliers in multivariate data, Journal of the Royal Statistical Society, Series B, 54. 761-771. 1992.
[2]	Atkinson, A. C., Fast very robust methods for the detection of multiple outliers, Journal of the American Statistical Association, 89. 1329-1339. 1994.
[3]	Hadi, A. S., Simonoff, J. S., Procedures for the identification of multiple outliers in linear models, Journal of the American Statistical Association, 88. 1264-1272. 1993.
[4]	Atkinson, A. C., Riani, M., Robust Diagnostic Regression Analysis, Springer, New York, 2000.
[5]	Atkinson, A. C., Riani, M., Forward search added-variable t-tests and the effect of masked outliers on model selection, Biometrika, 89(4). 939-946. 2002.
[6]	Atkinson, A. C., Riani, M., The Forward search and data visualization, Computational Statistics, 19. 29-54. 2004.
[7]	Atkinson, A. C., Riani, M., Cerioli, A., Exploring Multivariate Data with the Forward Search, Springer, New York, 2004.
[8]	Atkinson, A. C., Riani, M., Cerioli, A., The forward search: theory and data analysis, Journal of the Korean Statistical Society, 39. 117-134. 2010.
[9]	Bertaccini, B., Varriale, R., Robust Analysis of Variance: an approach based on the Forward, Computational statistics and data analysis, 51. 5172-5183. 2007.
[10]	Coin, D., Testing normality in the presence of outliers, Statistical Methods & Applications, 17. 3-12. 2008.
[11]	Riani, M., Atkinson, A.C., Cerioli, A., Finding an unknown number of multivariate outliers, Journal of the Royal Statistical Society Series, B 71. 447-466. 2009.
[12]	Bellini, T., Detecting atypical observations in financial data: the forward search for elliptical copulas, Advances in Data Analysis and Classification, 4. 287-299. 2010.
[13]	Grossi, L., Laurini, F., Robust estimation of efficient mean-variance frontiers, Advances in Data Analysis and Classification, 5. 3-22. 2011.
[14]	Torti, F., Perrotta, D., Atkinson, A.C., Riani, M., Benchmark testing of algorithms for very robust regression: FS, LMS and LTS, Computational statistics and data analysis, 56. 2501-2512. 2012.
[15]	Kolmogorov, A. N., Sulla Determinazione Empirica di Una Legge di Distribuzione, Giornale dell’Istituto Italiano degli Attuari, 4. 83-91. 1933.
[16]	Cramér, H., On the composition of elementary errors, Scandinavian Actuarial Journal, 11. 141-180. 1928.
[17]	Anderson, T. W., Darling, D. A., A Test of Goodness of Fit, Journal of the American Statistical Association, 49. 765-769. 1954.
[18]	Heiberg, A-C., Project at The Royal Veterinary and Agricultural University, 1999.
[19]	Huber, P.J., Robust Statistics, John Wiley & Sons, New York, 1981.