GloptiPolyRegion: Confidence region for optima of up to cubic polynomial models...

Description Usage Arguments Value Author(s) References Examples

Description

Computes and displays an approximated (1 - alpha) confidence region (CR) for the bound-constrained maximum of a polynomial regression model in up to cubic order with up to 5 controllable factors \insertCiteDelCastilloCROptimaRegion.

Usage

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GloptiPolyRegion(X, y, degree, lb, ub, B = 200, alpha = 0.05,
  maximization = TRUE, axes_labels = NULL,
  outputPDFFile = "CRplot.pdf", verbose = TRUE)

Arguments

X

numeric matrix of shape (N, k); N is the sample size; k is the number of variables, which can be 2, 3, 4 and 5; X specifies the design matrix

y

numeric vector of shape (N, 1); y specifies the responses

degree

integer scalor; degree specifies the order of the polynomial model, which can be 2 or 3

lb

numeric vector of shape (1, k); lb specifies the lower bounds for the k variables

ub

numeric vector of shape (1, k); ub specifies the upper bounds for the k variables

B

integer scalor; B specifies the number of bootstrap operations

alpha

numeric scalor between 0 and 1; alpha specifies the nominal confidence level, 1 - alpha, of the confidence region

maximization

boolean scalor; if specifies whether the algorithm computes the confidence region for the maxima or minima

axes_labels

vector of strings; it specifies the name of each experimental factor to be displayed on the CR plot; the default value is NULL, when the labels will be set to x1, x2, ...

outputPDFFile

name of the PDF file where the CR plot is saved (default: "CR_plot.pdf")

verbose

boolean scalor; it specifies whether to display running status

Value

Upon completion, a figure displaying the confidence region of the true optimum projected onto each pairwise-variable planes will be created (a pdf file will also be generated), and the function also returns a list consisting of 2 components:

boot_optima

numeric matrix of shape ((1 - alpha)B, k); it contains the (1 - alpha)B bootstrap optima

bagged_optimum

numeric vector of shape (1, k); the bagged optimum; computed by taking the column average of boot_optima

Author(s)

Enrique del Castillo exd13@psu.edu, Peng Chen pfc5098@psu.edu, Adam Meyers akm5733@psu.edu, John Hunt J.Hunt@exeter.ac.uk and James Rapkin jr297@exeter.ac.uk.

References

\insertAllCited

Examples

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## Not run: 
# Example 1: run GloptiPolyRegion on a quadratic, 3 vars example
out <- GloptiPolyRegion(
  X = quad_3D[, 1:3], y = quad_3D[, 4], degree = 2,
  lb = c(-2, -2, -2), ub = c(2, 2, 2), B = 500, alpha = 0.1,
  maximization = TRUE,
  outputPDFFile = "CR_quad_3D.pdf", verbose = TRUE
)
# check result
str(out)

# Example 2: run GloptiPolyRegion on a cubic, 5 vars example
out <- GloptiPolyRegion(
  X = cubic_5D$design_matrix, y = cubic_5D$response,
  degree = 3, lb = rep(0, 5), ub = rep(5, 5), B = 200,
  alpha = 0.05, maximization = TRUE,
  outputPDFFile = "CR_cubic_5D.pdf", verbose = TRUE
)
# check result
str(out)

## End(Not run)

OptimaRegion documentation built on July 3, 2019, 1:04 a.m.