R/OptimaRegion.R

In OptimaRegion: Confidence Regions for Optima of Response Surfaces

#' OptimaRegion package description
#'
#' OptimaRegion is a package for the computation of confidence regions on the location
#' of the optima of response surface models
#' \insertCite{DelCastilloCR}{OptimaRegion}.
#' 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 main functions:
#' OptRegionQuad, OptRegionTps, GloptiPolyRegion, CRcompare and GloptipolyR.
#'
#' OptRegionQuad computes distribution-free bootstrapped confidence regions for the
#' location of the optima of a quadratic polynomial model in 2 regressors.
#' OptRegionTps computes distribution-free bootstrapped confidence regions for 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
#' \insertCite{lasserre2001global}{OptimaRegion}
#' for global optimization of polynomial equations subject to bounds.
#'
#' @references{
#'   \insertAllCited{}
#' }
#' @importFrom Rdpack reprompt
#' @name OptimaRegion-package
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