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psiFindc

Find Tuning Constant(s) for "lqq" and "ggw" Psi Functions

Description

Find psi function tuning constant sets for "LQQ" and "GGW" psi (ψ) functions by specifying largest descent (minimal slope), efficiency and or breakdown point.

.psi.const() is called from lmrob.control() to set the tuning constants for psi and chi for "LQQ" and "GGW" psi. Unless the specified tuning constants are from fixed small set where the computations are stored precomputed, .psi.const() calls the corresponding .psi.<psi>.findc().

Usage

.psi.ggw.findc(ms, b, eff = NA, bp = NA,
               subdivisions = 100L,
               rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
               tol = .Machine$double.eps^0.25, ms.tol = tol/64, maxiter = 1000)

.psi.lqq.findc(ms, b.c, eff = NA, bp = NA,
               interval = c(0.1, 4), subdivisions = 100L,
               rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
               tol = .Machine$double.eps^0.25, maxiter = 1000)
.psi.const(cc, psi)

Arguments

`ms`	number, the minimal slope, typically negative.
`b, b.c`	number, specifying b or b/c for `"ggw"` or `"lqq"` respectively.
`eff`	a number (or `NA`), the desired efficiency, in [0,1] of the estimator. If `NA`, `bp` must be specified as valid number.
`bp`	a number (or `NA`), the desired breakdown point of the estimator, in [0,1].
`interval`	for finding c via `uniroot()`.
`subdivisions`	passed to `integrate()`.
`rel.tol, abs.tol`	relative and absolute tolerance for `integrate()`.
`tol`	relative tolerance for `uniroot()`.
`ms.tol`	relative tolerance for the internal `.psi.ggw.finda()`, eventually passed to `optimize` inside (internal) `.psi.ggw.mxs()`.
`maxiter`	maximal number of iterations for `uniroot()`.

`cc`	(for `.psi.const()`:) numeric vector of length 4, containing all constants `c(ms, b, eff, bp)`, where `b = b` for `"ggw"` and `b* = b.c` for `"lqq"`, and one of `(eff, bp)` is `NA`.
`psi`	a string, either `"ggw"` or `"lqq"`.

Details

For some important special cases, the result of .psi.*.findc() are stored precomputed for efficiency reasons. These cases are (the defaults for tuning.chi and tuning.psi respectively in lmrob.control()s result,

`tuning.chi`	`tuning.psi`
`c(-0.5, 1.5, NA, 0.5)`	`c(-0.5, 1.5, 0.95, NA)`

and for "ggw" additionally, these four cases:

`tuning.chi`	`tuning.psi`
	`c(-0.5, 1.5, 0.85, NA)`
`c(-0.5, 1, NA, 0.5)`	`c(-0.5, 1, 0.95, NA)`
	`c(-0.5, 1, 0.85, NA)`

Note that for "ggw", exactly these 2+4 = 6 cases also allow fast ρ and χ (aka rho~(.), see Mchi), function evaluations. For all other tuning constant settings, rho() evaluations are based on numerical integration via R's own Rdqags() C function (part of R's official API).

Value

a numeric vector of constants, for "lqq" or "ggw" psi functions, respectively:

"lqq":: (b, c, s) = (b/c * c, c, s = 1 - min_slope),
"ggw":: (0, a, b, c, rho(Inf)).

.psi.const(cc, psi) returns the argument cc with the above constant vectors as attribute "constants", in the case of psi = "lqq" in all cases (since robustbase version >= 0.93), for psi = "ggw" only in the non-standard cases.

Author(s)

Manuel Koller (original) and Martin Maechler (arguments, export, docs).

References

See the vignette about “psi-Functions Available in Robustbase”.

Examples

(c.ge95 <- .psi.ggw.findc(ms = -0.5, b = 1.5, eff = 0.95))
(c.ge90 <- .psi.ggw.findc(ms = -0.5, b = 1.5, eff = 0.90))
(c.gb50 <- .psi.ggw.findc(ms = -0.5, b = 1.5,  bp = 0.50))
stopifnot(all.equal(c.ge95, c(0, 1.386362,   1.5, 1.0628199,  4.7773893), tol = 1e-5),
          all.equal(c.ge90, c(0, 1.0282811,  1.5, 0.87086259, 3.2075233), tol = 1e-5),
          all.equal(c.gb50, c(0, 0.20367394, 1.5, 0.29591308, 0.37033962),tol = 1e-5))

(cl.e.95 <- .psi.lqq.findc(ms = -0.5, b.c = 1.5, eff = .95))
(cl.b.50 <- .psi.lqq.findc(ms = -0.5, b.c = 1.5,  bp = .50))
stopifnot(all.equal(cl.e.95, c(1.4734061,  0.98227073, 1.5), tol = 1e-5),
          all.equal(cl.b.50, c(0.40154568, 0.26769712, 1.5), tol = 1e-5))

robustbase

Basic Robust Statistics

v0.93-7

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian)

Initial release

2021-01-04