Análise de desenhos experimentais com outliers
Palavras-chave:
projetos compostos centrais, projetos robustos, outliers, minimax.Resumo
Objetivo principal do artigo é desenvolver projetos robustos outlier. De fato, o efeito negativo de outliers em qualquer ambiente experimental é estabelecido onde os outliers em qualquer ponto de design específico podem destruir os recursos do design para o qual ele está sendo desenvolvido. Neste artigo, tenta-se desenvolver uma versão de robustez para projetos compostos centrais que possam protegê-lo de outliers, introduzindo a ideia de efeito periférico minimax. Isso envolve o cálculo do grau de efeito (s) outlier (s) outlier (s) pode produzir e, em seguida, minimizar o máximo desses efeitos periféricos em uma tentativa de equalizar a influência de todos os pontos do projeto. Em comparação, esses designs robustos discrepantes são comprovadamente mais otimizados, nas escalas de otimalidades A, D e E, contra os designs convencionais rotacionais, ortogonais e outros existentes. Os designs robustos outlier, desenvolvidos aqui, são adequados para configurações propensas a outliers em que projetos convencionais não representam e analisam os processos e sistemas.
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Referências
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.
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
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Shabbir, M. S., Siddiqi, A. F., Kassim, N. M., Mustafa, F., & Abbas, M. (2019). Análise de desenhos experimentais com outliers. Amazonia Investiga, 8(18), 53–68. Recuperado de https://amazoniainvestiga.info/index.php/amazonia/article/view/258
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