Análisis de diseños experimentales con valores atípicos

Autores/as

  • Muhammad Salman Shabbir Universiti Sains Malaysia, Penang, Malaysia
  • Ahmed F. Siddiqi University of Central Punjab. Lahore, Pakistan
  • Normalini Md Kassim Universiti Sains Malaysia, Penang, Malaysia
  • Faisal Mustafa University of Central Punjab, Lahore Pakistan
  • Mazhar Abbas Department of Management Sciences. COMSATS University Islamabad, Vehari Campus

Palabras clave:

Diseños compuestos centrales, diseños robustos, valores atípicos, Minimax.

Resumen

El objetivo principal del artículo es desarrollar diseños robustos atípicos. De hecho, el efecto negativo de los valores atípicos en cualquier configuración experimental se establece donde los valores atípicos en cualquier punto de diseño específico pueden destruir las características del diseño para el que se está desarrollando. En este artículo se intenta desarrollar una versión de robustez para los diseños compuestos centrales que pueden protegerlo de los valores atípicos mediante la introducción de la idea del efecto periférico minimax. Esto implica el cálculo del grado de efecto (s) externo (s) que puede producir un valor atípico y luego minimizar el máximo de estos efectos externos en un intento de igualar la influencia de todos los puntos de diseño. En comparación, se demuestra que estos diseños robustos atípicos son más óptimos, en las escalas de las optimidades A, D y E, frente a los diseños convencionales existentes, ortogonales, rotativos y otros similares. Los diseños robustos atípicos, desarrollados aquí, son adecuados para configuraciones propensas a los valores atípicos en los que los diseños convencionales no representan ni analizan los procesos y sistemas.

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Biografía del autor/a

Muhammad Salman Shabbir, Universiti Sains Malaysia, Penang, Malaysia

Postdoctoral Fellow. School of Management. Universiti Sains Malaysia, Penang, Malaysia

Ahmed F. Siddiqi, University of Central Punjab. Lahore, Pakistan

UCP Business School. University of Central Punjab. Lahore, Pakistan

Normalini Md Kassim, Universiti Sains Malaysia, Penang, Malaysia

School of Management. Universiti Sains Malaysia, Penang, MalaysiaSchool of Management. Universiti Sains Malaysia, Penang, Malaysia

Faisal Mustafa, University of Central Punjab, Lahore Pakistan

UCP Business School. University of Central Punjab, Lahore Pakistan

Mazhar Abbas, Department of Management Sciences. COMSATS University Islamabad, Vehari Campus

Department of Management Sciences. COMSATS University Islamabad, Vehari Campus

Citas

Akhtar, M., & Prescott, P. (1986). Response surface designs robust to missing observations. Communications in Statistics-Simulation and Computation, 15(2), 345-363.

Atkinson, A., Donev, A., & Tobias, R. (2007). Optimum experimental designs, with SAS (Vol. 34). Oxford University Press.

Atkinson, A. C., Fedorov, V. V., Herzberg, A. M., & Zhang, R. (2014). Elemental information matrices and optimal experimental design for generalized regression models. Journal of Statistical Planning and Inference, 144, 81-91.

Barnett, V., & Lewis, T. (1964). Outliers in statistical data, Chichester: John Wiley, 1995. 584p.

Bay, S. D., & Schwabacher, M. (2003, August). Mining distance-based outliers in near linear time with randomization and a simple pruning rule. In Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 29-38). ACM.

Beckman, R. J., & Cook, R. D. (1983). Outlier………. s. Technometrics, 25(2), 119-149.

Box, G. E., & Draper, N. R. (1975). Robust designs. Biometrika, 347-352.

Box, G. E., & Draper, N. R. (1987). Empirical model-building and response surfaces. John Wiley & Sons.

Box, G. E., & Hunter, J. S. (1957). Multi-factor experimental designs for exploring response surfaces. The Annals of Mathematical Statistics, 28(1), 195-241.

Chang, L. C., Jones, D. K., & Pierpaoli, C. (2005). RESTORE: robust estimation of tensors by outlier rejection. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 53(5), 1088-1095.

Chatterjee, S., & Hadi, A. S. (1986). Influential observations, high leverage points, and outliers in linear regression. Statistical Science, 379-393.

Chauvenet, W. (1960). A Manual of Spherical and Practical Autonomy (Vol. II.

Cook, R. D., & Weisberg, S. (1980). Characterizations of an empirical influence function for detecting influential cases in regression. Technometrics, 22(4), 495-508.

Cook, R. D., & Weisberg, S. (1982). Residuals and influence in regression. New York: Chapman and Hall.

Cousineau, D., & Chartier, S. (2010). Outliers detection and treatment: a review. International Journal of Psychological Research, 3(1), 58-67.

Daniell, P. J. (1920). Observations weighted according to order. American Journal of Mathematics, 42(4), 222-236.
Dixon, W. J. (1950). Analysis of extreme values. The Annals of Mathematical Statistics, 21(4), 488-506.

Edgeworth, F. Y. (1887). Xli. on discordant observations. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 23(143), 364-375.

Eubank, R. L. (1984). The hat matrix for smoothing splines. Statistics & probability letters, 2(1), 9-14.

Festing, M. F., & Altman, D. G. (2002). Guidelines for the design and statistical analysis of experiments using laboratory animals. ILAR journal, 43(4), 244-258.

RA Fisher, M. A. (1922). On the mathematical foundations of theoretical statistics. Phil. Trans. R. Soc. Lond. A, 222(594-604), 309-368.

Gao, G., & Yang, J. (2015, June). Matrix Based Regression with Local Position-Patch and Nonlocal Similarity for Face Hallucination. In International Conference on Intelligent Science and Big Data Engineering (pp. 110-117). Springer, Cham.

Geramita, A. V., Geramita, J. M., & Wallis, J. S. (1976). Orthogonal desingns. Linear and Multilinear Algebra, 3(4), 281-306.

Glaisher, J. W. L. (1873). On the rejection of discordant observations. Monthly Notices of the Royal Astronomical Society, 33, 391-402.

GLAISHER, J. 1874. Note on a Paper by Mr. Stone; On the Rejection of Discordanr Observations. Monthly Notices of the Royal Astronomical Society, 24, 251.

Gould, B. A. (1855). On Peirce's Criterion for the Rejection of Doubtful Observations, with tables for facilitating its application. The Astronomical Journal, 4, 81-87.

Grubbs, F. E. (1950). Sample criteria for testing outlying observations. The Annals of Mathematical Statistics, 21(1), 27-58.

Heo, G., Schmuland, B., & Wiens, D. P. (2001). Restricted minimax robust designs for misspecified regression models. Canadian Journal of Statistics, 29(1), 117-128.

Hoaglin, D. C., & Welsch, R. E. (1978). The hat matrix in regression and ANOVA. The American Statistician, 32(1), 17-22.

Irwin, J. O. (1925). On a criterion for the rejection of outlying observations. Biometrika, 238-250.

Jauffret, C. (2007). Observability and Fisher information matrix in nonlinear regression. IEEE Transactions on Aerospace and Electronic Systems, 43(2), 756-759.

Kiefer, J. (1985). Collected Papers III: design of experiments. Springer-Verlag.

Knorr, E. M., Ng, R. T., & Tucakov, V. (2000). Distance-based outliers: algorithms and applications. The VLDB Journal—The International Journal on Very Large Data Bases, 8(3-4), 237-253.

Montgomery, D. C., & Myers, R. H. (1995). Response surface methodology: process and product optimization using designed experiments, Raymond H. Meyers, Douglas C. Montgomery, A Wiley-Interscience Publications.

Mukerjee, R., & Huda, S. (1985). Minimax second-and third-order designs to estimate the slope of a response surface. Biometrika, 72(1), 173-178.

Newcomb, S. (1886). A generalized theory of the combination of observations so as to obtain the best result. American journal of Mathematics, 343-366.

Peirce, B. (1852). Criterion for the rejection of doubtful observations. The Astronomical Journal, 2, 161-163.

Peirce, B. (1877, May). On Peirce's criterion. In Proceedings of the American Academy of Arts and Sciences (Vol. 13, pp. 348-351). American Academy of Arts & Sciences.

Rao, C. R., & Mitra, S. K. (1973). Theory and application of constrained inverse of matrices. SIAM Journal on Applied Mathematics, 24(4), 473-488.

Rao, C. R., & Rao, M. B. (1998). Matrix algebra and its applications to statistics and econometrics. World Scientific.

Rao, C. R., & Toutenburg, H. (1995). Linear models. In Linear models (pp. 3-18). Springer, New York, NY.

Saunder, S. A. (1903). Note on the use of Peirce's criterion for the rejection of doubtful observations. Monthly Notices of the Royal Astronomical Society, 63, 432-436.

Shannon, C. E. (1948). A mathematical theory of communication. Bell system technical journal, 27(3), 379-423.

Siddiqi, A. F. (2003). Outliers in Designed Experiments; Classical Robust & Resistant Methods. Journal of Statistics, 10, 49-65.

Siddiqi, A. F. (2008). Outlier robust designs. International Journal of Applied Mathematics and Statistics™, 13(M08), 64-77.

Siddiqi, A. F. (2010). Outlier Robust Draper & Lin Designs. Pakistan Journal of Statistics and Operation Research, 7(1), 87-99.

Sitter, R. R. (1992). Robust designs for binary data. Biometrics, 1145-1155.
STUDENT 1927. Errors of routine analysis. Biometrika, 151-164.

Thompson, W. R. (1935). On a criterion for the rejection of observations and the distribution of the ratio of deviation to sample standard deviation. The Annals of Mathematical Statistics, 6(4), 214-219.

Wiens, D. P. (1990). Robust minimax designs for multiple linear regression. Linear algebra and its applications, 127, 327-340.

Wiens, D. P. (1992). Minimax designs for approximately linear regression. Journal of Statistical Planning and Inference, 31(3), 353-371.

Winlock, J. (1856). On Professor Airy's objections to Peirce's criterion. The Astronomical Journal, 4, 145-147.

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Publicado

2019-02-27

Cómo citar

Shabbir, M. S., Siddiqi, A. F., Kassim, N. M., Mustafa, F., & Abbas, M. (2019). Análisis de diseños experimentales con valores atípicos. Amazonia Investiga, 8(18), 53–68. Recuperado a partir de https://amazoniainvestiga.info/index.php/amazonia/article/view/258

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