internal-interpolate: Internal helper functions for generating interpolation grids...
In ROptEst: Optimally Robust Estimation

internal_interpolate_helpers

R Documentation

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.