OptimaRegion is a package for the computation of confidence regions on the location of the optima of response surface models \insertCiteDelCastilloCROptimaRegion. Both parametric (quadratic polynomial) and nonparametric (thin plate spline) models are supported. The confidence regions obtained do not rely on any distributional assumption, such as Normality of the response, and are obtained by bootstrapping. The resulting regions are both valid and unbiased, and have a size that rapidly decreases as the sample size increases. Regions are obtained both numerically (as a set of points) and graphically, as the convex hull of the points. Functionality for the computation of a bootstrap confidence interval on the distance between the optima of two different response surfaces is included.
The OptimaRegion package provides five important functions: OptRegionQuad, OptRegionTps, GloptiPolyRegion, CRcompare and GloptipolyR.
OptRegionQuad computes distribution-free bootstrapped confidence regionsfor the location of the optima of a quadratic polynomial model in 2 regressors. OptRegionTps computes distribution-free bootstrapped confidence regionsfor the location of the optima of a Thin Plate Spline model in 2 regressors. GloptiPolyRegion computes distribution-free bootstrapped CRs for the location of global optima for polynomial models up to cubic order in up to 5 regressors. CRcompare computes bootstrapped confidence intervals for the distance between the optima of two different response surface models, either quadratic polynomials or thin plate spline models. GloptipolyR is an R implementation of the “Gloptipoly” algorithm \insertCitelasserre2001globalOptimaRegion for global optimization of polynomial equations subject to bounds.
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