TY - JOUR
T1 - Confidence regions for the location of response surface optima : the R package OptimaRegion
AU - del Castillo, Enrique
AU - Chen, Peng
AU - Meyers, Adam
AU - Hunt, John
AU - Rapkin, James
PY - 2022
Y1 - 2022
N2 - Statistical inference on the location of the optima (global maxima or minima) is one of the main goals in the area of Response Surface Methodology, with many applications in engineering and science. While there exist previous methods for computing confidence regions on the location of optima, these are for linear models based on a Normal distribution assumption, and do not address specifically the difficulties associated with guaranteeing global optimality. This paper describes distribution-free methods for the computation of confidence regions on the location of the global optima of response surface models. The methods are based on bootstrapping and Tukey’s data depth, and therefore their performance does not rely on distributional assumptions about the errors affecting the response. An R language implementation, the package OptimaRegion, is described. Both parametric (quadratic and cubic polynomials in up to 5 covariates) and nonparametric models (thin plate splines in 2 covariates) are supported. A coverage analysis is presented demonstrating the quality of the regions found. The package also contains an R implementation of the Gloptipoly algorithm for the global optimization of polynomial responses subject to bounds.
AB - Statistical inference on the location of the optima (global maxima or minima) is one of the main goals in the area of Response Surface Methodology, with many applications in engineering and science. While there exist previous methods for computing confidence regions on the location of optima, these are for linear models based on a Normal distribution assumption, and do not address specifically the difficulties associated with guaranteeing global optimality. This paper describes distribution-free methods for the computation of confidence regions on the location of the global optima of response surface models. The methods are based on bootstrapping and Tukey’s data depth, and therefore their performance does not rely on distributional assumptions about the errors affecting the response. An R language implementation, the package OptimaRegion, is described. Both parametric (quadratic and cubic polynomials in up to 5 covariates) and nonparametric models (thin plate splines in 2 covariates) are supported. A coverage analysis is presented demonstrating the quality of the regions found. The package also contains an R implementation of the Gloptipoly algorithm for the global optimization of polynomial responses subject to bounds.
UR - https://hdl.handle.net/1959.7/uws:75143
U2 - 10.1080/03610918.2020.1823412
DO - 10.1080/03610918.2020.1823412
M3 - Article
SN - 0361-0918
VL - 51
SP - 7074
EP - 7094
JO - Communications in Statistics: Simulation and Computation
JF - Communications in Statistics: Simulation and Computation
IS - 12
ER -