Model-Robust Designs for Quantile Regression

We give methods for the construction of designs for regression models, when the purpose of the investigation is the estimation of the conditional quantile function, and the estimation method is quantile regression. The designs are robust against misspecified response functions, and against unanticipated heteroscedasticity. The methods are illustrated by example, and in a case study in which they are applied to growth charts.

[1]  Jane J. Ye,et al.  for misspecified regression models , 2003 .

[2]  Holger Dette,et al.  Optimal designs for testing the functional form of a regression via nonparametric estimation techniques , 2001 .

[3]  Douglas P. Wiens,et al.  A comparative study of robust designs for M-estimated regression models , 2010, Comput. Stat. Data Anal..

[4]  W. Bischoff.  An Improvement in the Lack-of-Fit Optimality of the (Absolutely) Continuous Uniform Design in Respect of Exact Designs , 2010 .

[5]  W M Moore,et al.  Physical growth: National Center for Health Statistics percentiles. , 1979, The American journal of clinical nutrition.

[6]  J. Roca-Pardiñas,et al.  Flexible quantile regression models: application to the study of the purple sea urchin , 2013 .

[7]  Douglas P. Wiens.  Bias Constrained Minimax Robust Designs for Misspecified Regression Models , 2000 .

[8]  Techniques for the construction of robust regression designs , 2013 .

[9]  Keith Knight,et al.  Limiting distributions for $L\sb 1$ regression estimators under general conditions , 1998 .

[10]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[11]  R. Koenker,et al.  Quantile regression methods for reference growth charts , 2006, Statistics in medicine.

[12]  Pengfei Li,et al.  Robustness of design in dose–response studies , 2011 .

[13]  D. Pollard.  Asymptotics for Least Absolute Deviation Regression Estimators , 1991, Econometric Theory.

[14]  Arnold J. Stromberg,et al.  Number-theoretic Methods in Statistics , 1996 .

[15]  R. Koenker,et al.  Regression Quantiles , 2007 .

[16]  Holger Dette,et al.  Optimal Designs for Quantile Regression Models , 2012 .

[17]  D. G. Simpson,et al.  On One-Step GM Estimates and Stability of Inferences in Linear Regression , 1992 .

[18]  David C. Woods,et al.  Designs for Generalized Linear Models With Several Variables and Model Uncertainty , 2006, Technometrics.

[19]  D. Wiens.  Robust weights and designs for biased regression models: Least squares and generalized M-estimation , 2000 .

[20]  Yanyuan Ma,et al.  ANALYSIS ON CENSORED QUANTILE RESIDUAL LIFE MODEL VIA SPLINE SMOOTHING. , 2012, Statistica Sinica.

[21]  D. Wiens,et al.  Integer-Valued, Minimax Robust Designs for Estimation and Extrapolation in Heteroscedastic, Approximately Linear Models , 2000 .

[22]  Ker-Chau Li,et al.  Robust Regression Designs when the Design Space Consists of Finitely Many Points , 1984 .

[23]  Linglong Kong,et al.  Quantile tomography: using quantiles with multivariate data , 2008, Statistica Sinica.

[24]  Vladimir K. Kaishev,et al.  Optimal experimental designs for the B -spline regression , 1989 .

[25]  D. Wiens.  Designs for approximately linear regression: two optimality properties of uniform designs , 1991 .

[26]  A. Pere.  Comparison of two methods for transforming height and weight to Normality , 2000, Annals of human biology.

[27]  Weng Kee Wong,et al.  On the Equivalence of Constrained and Compound Optimal Designs , 1994 .

[28]  W. K. Yuen,et al.  Applications and Implementations of Continuous Robust Designs , 2011 .

[29]  G. Claeskens,et al.  Focused Model Selection in Quantile Regression , 2013 .

[30]  R. Koenker.  Quantile Regression: Name Index , 2005 .

[31]  G. Box,et al.  A Basis for the Selection of a Response Surface Design , 1959 .

[32]  V. Yohai,et al.  Asymptotic behavior of general M-estimates for regression and scale with random carriers , 1981 .

[33]  Xuming He,et al.  Conditional growth charts , 2006 .

[34]  A. Rubia,et al.  On downside risk predictability through liquidity and trading activity: A dynamic quantile approach , 2013 .

[35]  Douglas P. Wiens,et al.  Restricted minimax robust designs for misspecified regression models , 2001 .

[36]  Douglas P. Wiens,et al.  Robust model-based sampling designs , 2013, Stat. Comput..

[37]  Douglas P. Wiens,et al.  Minimax designs for approximately linear regression , 1992 .