internal-interpolate: Internal helper functions for generating interpolation grids...

In ROptEst: Optimally Robust Estimation

Internal helper functions for generating interpolation grids for speed up in package ROptEst

Description

These functions are used internally to generate interpolation grids, for Lagrange multipliers or LDEstimators in package RobExtremes, to be stored in the respective ‘sysdata.rda’ file.

Usage

.RMXE.th(th, PFam, modifyfct, loRad = 0, upRad = Inf, z.start = NULL,
             A.start = NULL, upper = NULL, lower = NULL,
             OptOrIter = "iterate", maxiter = 50,
             tol = .Machine$double.eps^0.4, loRad0 = 1e-3, ...)
.MBRE.th(th, PFam, modifyfct,
             z.start = NULL, A.start = NULL, upper = 1e4,
             lower = 1e-4, OptOrIter = "iterate",
             maxiter = 50, tol = .Machine$double.eps^0.4, ...)
.OMSE.th(th, PFam, modifyfct, radius = 0.5,
             z.start = NULL, A.start = NULL, upper = 1e4,
             lower = 1e-4, OptOrIter = "iterate",
             maxiter = 50, tol = .Machine$double.eps^0.4, ...)

.getLMGrid(thGrid, PFam, optFct = .RMXE.th, modifyfct, radius = 0.5,
           GridFileName = "LMGrid.Rdata", withPrint = FALSE,
           upper = 1e4, lower = 1e-4, OptOrIter = "iterate",
           maxiter = 50, tol = .Machine$double.eps^0.4,
           loRad = 0, upRad = Inf, loRad0 = 1e-3,
           loRad.s = 0.2, upRad.s = 1, withStartLM = TRUE, len = 13)


.saveGridToCSV(Grid, toFileCSV, namPFam, nameInSysdata)

.readGridFromCSV(fromFileCSV)

.generateInterpGrid(thGrid, PFam, toFileCSV = "temp.csv",
            getFun = .getLMGrid, ..., modifyfct, nameInSysdata,
            GridFileName, withPrint = TRUE, len = 13)

Arguments

th	numeric of length 1; the grid value at which to compute LMs.
PFam	an object of class "ParamFamily", the parametric family at which to evaluate the Lagrange multipliers or LDEstimators; in our use case, it is a shape-scale model, hence the respective (main) parameter must contain "scale" and "shape".
modifyfct	function with arguments th and PFam to move the parametric family to the point of the grid value; returns the moved parametric family.
radius	[for OMSE]: positive numeric of length 1: the radius of the neighborhood for which the LM's are to be computed; defaults to 0.5.
loRad	the lower end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).
upRad	the upper end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).
loRad.s	the lower end point of the interval to be searched in the outer optimization (for the user-guessed radius); if NULL set to loRad in the algorithm.
upRad.s	the upper end point of the interval to be searched in the outer optimization (for the user-guessed radius); if NULL set to upRad in the algorithm.
z.start	initial value for the centering constant.
A.start	initial value for the standardizing matrix.
upper	upper bound for the optimal clipping bound.
lower	lower bound for the optimal clipping bound.
OptOrIter	character; which method to be used for determining Lagrange multipliers A and a: if (partially) matched to "optimize", getLagrangeMultByOptim is used; otherwise: by default, or if matched to "iterate" or to "doubleiterate", getLagrangeMultByIter is used. More specifically, when using getLagrangeMultByIter, and if argument risk is of class "asGRisk", by default and if matched to "iterate" we use only one (inner) iteration, if matched to "doubleiterate" we use up to Maxiter (inner) iterations.
maxiter	the maximum number of iterations.
tol	the desired accuracy (convergence tolerance).
loRad0	for numerical reasons: the effective lower bound for the zero search; internally set to max(loRad,loRad0).
withStartLM	logical of length 1: shall the LM's of the preceding grid value serve as starting value for the next grid value?
withPrint	logical of length 1: shall current grid value be printed out?
thGrid	numeric; grid values.
optFct	function with arguments theta, PFam, and modifyfct; determines the Lagrange multipliers.
GridFileName	character; if GridFileName!="", the pure y-grid values are saved under this filename.
Grid	numeric; grid matrix (x- and y-values).
toFileCSV	character; name of the csv file to which the grid is written.
namPFam	character; name of the parametric family for which the grid was generated.
nameInSysdata	character; grid name (e.g., 'OMSE', 'Sn') for which the grid was generated.
fromFileCSV	character; name of the csv file from which the grid is read.
getFun	function with first argument th, second argument PFam and last arguments GridFileName, withPrint; produces the y-values for the interpolation grid.
...	further arguments to be passed on, e.g., to getFun.
len	integer; number of Lagrange multipliers to be calibrated.

Details

.MBRE.th computes the Lagrange multipliers for the MBRE estimator, .OMSE.th for the OMSE estimator at radius radius, and .RMXE.th the RMXE estimator.

.getLMGrid in a large loop computes the Lagrange multipliers for optimally robust IFs for each element of a given grid.

.saveGridToCSV saves a given grid to a csv file, and in addition, in a file with same name but with file extension ".txt" writes the parametric family and the grid name.

.readGridFromCSV reads in a grid from a csv file together with the information given in the corresponding ".txt" file.

.generateInterpGrid by means of calls to function-argument getFun (e.g. getLMGrid computes the grid, if desired smoothes it, and then saves it to .csv.

Value

.MBRE.th	A list with items b (a number; clipping height), a (a 2-vector; outer centering), a.w (a 2-vector; inner centering, in the weight), A (a 2x2 matrix; outer standardization), A.w (a 2x2 matrix; inner standardization, in the weight).
.OMSE.th	as .MBRE.th.
.RMXE.th	as .MBRE.th.
.getLMGrid	A grid (in form of a matrix of x and y-values) pasted together by cbind.
.saveGridToCSV	invisible(NULL).
.readGridFromCSV	a list with the read-in items, i.e., an item Grid with the grid, an item namPFam with the name of the parametric family, and namInSysdata, the name of the read in grid.
.generateInterpGrid	invisible(NULL).

Note

These functions are only meant for the developers of package ROptEst (or respective packages). They can be used to speed up things by interpolation. Our use case is a speed up for further scale-shape families (or enhance existing speed-ups) such that the respective grids are stored in a ‘sysdata.rda’ file of an external package RobAStRda —see mail exchange P.Ruckdeschel - U.Ligges on R-devel— https://stat.ethz.ch/pipermail/r-devel/2013-February/065794.html. Special attention has to be paid for R-versions pre and post R-2.16 which is why we use .versionSuff.

ROptEst documentation built on Sept. 12, 2024, 7:40 a.m.