Efficient Mixture Design Fitting Quadratic Surface with Quantile Responses Using First-degree Polynomial

References

• Bassett, G., Koenker, R. (1982). An empirical quantile function for linear models with i.i.d. errors. Journal of the American Statistical Association 77:407–415.
   Web of Science ®Google Scholar
• Becker, N.G. (1968). Models for the response of a mixtures. Journal of Royal Statistical Society: Series B 30:349–358.
   Google Scholar
• Becker, N.G. (1970). Mixture designs for model linear in the proportions. Biometrika 57(2):329–338.
   Web of Science ®Google Scholar
• Box, G.E., Draper, N.R. (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association 54:622–654.
   Web of Science ®Google Scholar
• Buchinsky, M. (2006). Recent advances in quantile regression models: A practical guideline for empirical research. The Journal of Human Resources 33(1):88–126.
   Web of Science ®Google Scholar
• Dette, H., Trampisch, M. (2012). Optimal designs for quantile regression models. Journal of the American Statistical Association 107(499):1140–1151.
   Web of Science ®Google Scholar
• Dette, H., Bretz, F., Pepelyshev, A., Pinheiro, J. (2008). Optimal designs for dose-finding studies. Journal of the American Statistical Association 103(483):1225–1237.
   Web of Science ®Google Scholar
• Dette, H., Kiss, C., Bevanda, M., Bretz, F. (2010). Optimal designs for the EMAX, log-linear and exponential models. Biometrika 97(2):513–518.
   Web of Science ®Google Scholar
• Draper, N.R., Lawrence, W.E. (1965). Mixture designs for three factors. Journal of the Royal Statistical Society: Series B 27:450–465.
   Google Scholar
• Draper, N.R., Pukelsheim, F. (1999). Kiefer ordering of simplex designs for first and second degree mixture models. Journal of Statistical Planning and Inference 79:325–348.
   Web of Science ®Google Scholar
• Gourieroux, C., Laurent, J.P., Scaillet, O. (2000). Sensitivity analysis of values at risk. Journal of Empirical Finance 7:225–245.
   Google Scholar
• Guan, Y., Chao, X. (1987). On the A-optimal allocation of observations for the generalized simplex-centroid design (in Chinese). Journal of Engineering Mathematics 4:33–39.
   Google Scholar
• Hosseini, R. (2010). Approximating quantiles in very large datasets. Available at: http://arxiv.org/pdf /1007.1032.pdf.
   Google Scholar
• Huang, M.N., Hsu, H.L., Chou, C.J., Klein, T. (2009). Model robust D- and A-optimal designs for mixture experiments. Statistica Sinica 19:1055–1075.
   Web of Science ®Google Scholar
• Kiefer, J.C. (1961). Optimum designs in regression problems, II. Annals of Mathematical Statistics 32:298–325.
   Google Scholar
• Kiefer, J. (1974). General equivalence theory for optimum design (approximate theory). The Annals of Statistics 2:849–879.
   Web of Science ®Google Scholar
• Kiefer, J., Wolfowitz, J. (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics 12:363–366.
   Google Scholar
• Koenker, R. (2005). Quantile Regression. New York: Cambridge University Press.
   Google Scholar
• Koenker, R., Bassett, G. (1978). Regression quantiles. Econometrica 46(1):33–50.
   Web of Science ®Google Scholar
• Koenker, R., Bassett, G. (1982). Test of linear hypotheses and l1 estimation. Econometrica 50(6):1577–1582.
   Web of Science ®Google Scholar
• Koenker, R., Hallock, K. (2001). Quantile regression: An introduction, Journal of Economic Perspectives 15:143–156.
   Web of Science ®Google Scholar
• Koenker, R., Machado, J. (1999). Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association 94:448, 1296–1310.
   Google Scholar
• Martin, R., Thompson, K., Browne, C. (2001). VAR: Who contributes and how much? RISK 14:99–102.
   Google Scholar
• Parzen, E. (1979). Nonparametric statistical data modeling. Journal of the American Statistical Association 74:105–121.
   Web of Science ®Google Scholar
• Rychlik, T. (2001). Projecting Statistical Functionals. New York: Springer.
   Google Scholar
• Scheffé, H. (1958). Experiments with mixtures. Journal of Royal Statistical Society: Series B 20:344–360.
   Google Scholar
• Scheffé, H. (1963). Simplex-centroid designs for experiments with mixtures. Journal of Royal Statistical Society: Series B, 25:235–263.
   Google Scholar