# Function to compute LD (location-dispersion) estimates

### Description

Function `LDEstimator`

provides a general way to compute
estimates for a given parametric family of probability measures
(with a scale and shape parameter) which
can be obtained by matching location and dispersion functionals
against empirical counterparts.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
LDEstimator(x, loc.est, disp.est, loc.fctal, disp.fctal, ParamFamily,
loc.est.ctrl = NULL, loc.fctal.ctrl=NULL,
disp.est.ctrl = NULL, disp.fctal.ctrl=NULL,
q.lo =1e-3, q.up=15, log.q =TRUE,
name, Infos, asvar = NULL, nuis.idx = NULL,
trafo = NULL, fixed = NULL, asvar.fct = NULL, na.rm = TRUE,
..., .withEvalAsVar = FALSE, vdbg = FALSE)
medkMAD(x, ParamFamily, k=1, q.lo =1e-3, q.up=15, nuis.idx = NULL,
trafo = NULL, fixed = NULL, asvar.fct = NULL, na.rm = TRUE,
..., .withEvalAsVar = FALSE, vdbg = FALSE)
medkMADhybr(x, ParamFamily, k=1, q.lo =1e-3, q.up=15, KK = 20, nuis.idx = NULL,
trafo = NULL, fixed = NULL, asvar.fct = NULL, na.rm = TRUE,
..., .withEvalAsVar = FALSE)
medSn(x, ParamFamily, q.lo =1e-3, q.up=10, nuis.idx = NULL,
trafo = NULL, fixed = NULL, asvar.fct = NULL, na.rm = TRUE,
accuracy = 100, ..., .withEvalAsVar = FALSE)
medQn(x, ParamFamily, q.lo =1e-3, q.up=15, nuis.idx = NULL,
trafo = NULL, fixed = NULL, asvar.fct = NULL, na.rm = TRUE,
..., .withEvalAsVar = FALSE)
``` |

### Arguments

`x` |
(empirical) data |

`ParamFamily` |
an object of class |

`loc.est` |
a function expecting |

`disp.est` |
a function expecting |

`loc.fctal` |
a function expecting a distribution object as first argument; location functional. |

`disp.fctal` |
a function expecting a distribution object as first argument; dispersion functional; may only take non-negative values. |

`loc.est.ctrl` |
a list (or |

`disp.est.ctrl` |
a list (or |

`loc.fctal.ctrl` |
a list (or |

`disp.fctal.ctrl` |
a list (or |

`k` |
numeric; additional parameter for |

`KK` |
numeric; Maximal number of trials with different |

`q.lo` |
numeric; lower bound for search intervall in shape parameter. |

`q.up` |
numeric; upper bound for search intervall in shape parameter. |

`log.q` |
logical; shall the zero search be done on log-scale? |

`name` |
optional name for estimator. |

`Infos` |
character: optional informations about estimator |

`asvar` |
optionally the asymptotic (co)variance of the estimator |

`nuis.idx` |
optionally the indices of the estimate belonging to nuisance parameter |

`fixed` |
optionally (numeric) the fixed part of the parameter |

`trafo` |
an object of class |

`asvar.fct` |
optionally: a function to determine the corresponding
asymptotic variance; if given, |

`na.rm` |
logical: if |

`accuracy` |
numeric: argument to be passed on to |

`...` |
further arguments to be passed to location estimator and functional and dispersion estimator and functional. |

`vdbg` |
logical; if |

`.withEvalAsVar` |
logical: shall slot |

### Details

The arguments `loc.est`

, `disp.est`

(location and dispersion estimators)
have to be functions with first argument `x`

(a numeric vector with the
empirical data) and additional, optional individual arguments to be passed on
in the respective calls as lists `loc.est.ctrl`

, `disp.est.ctrl`

,
and global additional arguments through the `...`

argument.
Similarly, arguments `loc.fctal`

, `disp.fctal`

(location and
dispersion functionals) have to be functions with first argument an
object of class `UnivariateDistribution`

, and additional, optional
individual arguments to be passed on
in the respective calls as lists `loc.fctal.ctrl`

, `disp.fctal.ctrl`

,
and global additional arguments again through the `...`

argument.
Uses `.LDMatch`

internally.

### Value

An object of S4-class `"Estimate"`

.

### Note

The values for `q.lo`

and `q.up`

are a bit delicate and
have to be found, model by model, by try and error.
As a rule, `medSn`

is rather slow, as the evaluation of the `Sn`

functional is quite expensive. So if `medSn`

is the estimator of choice,
it pays off, for a given shape-scale family, to evaluate `medSn`

on a
grid of shape-values (with scale 1) and then to use an interpolation techniques
in a particular method to replace the default one for this shape-scale family.
As an example, we have done so for the GPD family.

### Author(s)

Nataliya Horbenko Nataliya.Horbenko@itwm.fraunhofer.de,

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### References

P. Ruckdeschel, N. Horbenko (2011): Yet another breakdown point notion: EFSBP –illustrated at scale-shape models. ArXiv 1005.1480. To appear at Metrika. DOI: 10.1007/s00184-011-0366-4.

A. Marazzi and C. Ruffieux (1999): The truncated mean of asymmetric distribution. Computational Statistics and Data Analysis 32: 79-100 .

### See Also

`ParamFamily-class`

, `ParamFamily`

,
`Estimate-class`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
## (empirical) Data
set.seed(123)
x <- rgamma(50, scale = 0.5, shape = 3)
## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)
medQn(x = x, ParamFamily = G)
medSn(x = x, ParamFamily = G, q.lo = 0.5, q.up = 4)
## Not run:
## without speedup for Sn:
LDEstimator(x, loc.est = median, disp.est = Sn, loc.fctal = median,
disp.fctal = getMethod("Sn","UnivariateDistribution"),
ParamFamily = G, disp.est.ctrl = list(constant=1))
## End(Not run)
medkMAD(x = x, ParamFamily = G)
medkMADhybr(x = x, ParamFamily = G)
medkMAD(x = x, k=10, ParamFamily = G)
##not at all robust:
LDEstimator(x, loc.est = mean, disp.est = sd,
loc.fctal = E, disp.fctal = sd,
ParamFamily = G)
``` |

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