L2ParamFamily: Generating function for L2ParamFamily-class
In distrMod: Object Oriented Implementation of Probability Models

L2ParamFamily

R Documentation

Generating function for L2ParamFamily-class

Description

Generates an object of class "L2ParamFamily".

Usage

L2ParamFamily(name, distribution = Norm(), distrSymm, 
              main = main(param), nuisance = nuisance(param),
              fixed = fixed(param), trafo = trafo(param),
              param = ParamFamParameter(name = paste("Parameter of", name),  
                          main = main, nuisance = nuisance, 
                          fixed = fixed, trafo = trafo),
              props = character(0),
              startPar = NULL, makeOKPar = NULL,
              modifyParam = function(theta){ Norm(mean=theta) },
              L2deriv.fct = function(param) {force(theta <- param@main)
                           return(function(x) {x-theta})},
              L2derivSymm, L2derivDistr, L2derivDistrSymm, 
              FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
              .returnClsName = NULL, .withMDE = TRUE)

Arguments

`name`	character string: name of the family
`distribution`	object of class `"Distribution"`: member of the family
`distrSymm`	object of class `"DistributionSymmetry"`: symmetry of `distribution`.
`main`	numeric vector: main parameter
`nuisance`	numeric vector: nuisance parameter
`fixed`	numeric vector: fixed part of the parameter
`trafo`	function in `param` or matrix: transformation of the parameter
`param`	object of class `"ParamFamParameter"`: parameter of the family
`startPar`	`startPar` is a function in the observations `x` returning initial information for `MCEstimator` used by `optimize` resp. `optim`; i.e; if (total) parameter is of length 1, `startPar` returns a search interval, else it returns an initial parameter value.
`makeOKPar`	`makeOKPar` is a function in the (total) parameter `param`; used if `optim` resp. `optimize`— try to use “illegal” parameter values; then `makeOKPar` makes a valid parameter value out of the illegal one; if `NULL` slot `makeOKPar` of `ParamFamily` is used to produce it.
`modifyParam`	function: mapping from the parameter space (represented by `"param"`) to the distribution space (represented by `"distribution"`).
`props`	character vector: properties of the family
`L2deriv.fct`	function: mapping from the parameter space (argument `param` of class `"ParamFamParameter"`) to a mapping from observation `x` to the value of the L2derivative; `L2deriv.fct` is used by `modifyModel` to move the L2deriv according to a change in the parameter, and to fill slot `L2deriv`. More specifically, let us call the parts `main` and `nuisance` of the parameter the unknown parameter. If this unknown parameter is one-dimensional, the return value of `L2deriv.fct` must be a function in argument `x`, which is vectorized, (i.e., callable for a vector-valued `x`), and has a one-dimensional, numeric return value. In case the dimension of the unknown parameter is larger than one, the return value must be a list of functions, each of which satisfies the conditions formulated for the case of a one-dimensional parameter of interest. The order of the components of this list is the same as the order of the parameter coordinates in `main`, followed by the ones in `nuisance`.
`L2derivSymm`	object of class `"FunSymmList"`: symmetry of the maps contained in `L2deriv`; a list of symmetry properties of the same length as the return value of `L2deriv.fct` .
`L2derivDistr`	object of class `"UnivarDistrList"`: distribution of `L2deriv`; the length of this list of univariate distributions must be of the same length as the return value of `L2deriv.fct` .
`L2derivDistrSymm`	object of class `"DistrSymmList"`: symmetry of the distributions contained in `L2derivDistr`; the length of this list of symmetry properties must be of the same length as the return value of `L2deriv.fct` .
`FisherInfo.fct`	function: mapping from the parameter space (argument `param` of class `"ParamFamParameter"`) to the set of positive semidefinite matrices; `FisherInfo.fct` is used by `modifyModel` to move the Fisher information according to a change in the parameter
`FisherInfo`	object of class `"PosSemDefSymmMatrix"`: Fisher information of the family
`.returnClsName`	the class name of the return value; by default this argument is `NULL` whereupon the return class will be `L2ParamFamily`; but, internally, this generating function is also used to e.g. produce objects of class `BinomialFamily`, `PoisFamily` `GammaFamily`, `BetaFamily`.
`.withMDE`	logical of length 1: Tells R how to use the function from slot `startPar` in case of a `kStepEstimator`—use it as is or to compute the starting point for a minimum distance estimator which in turn then serves as starting point for `roptest` / `robest` (from package ROptEst). If `TRUE` (default) the latter alternative is used. Ignored if ROptEst is not used.

Details

If name is missing, the default “L2 differentiable parametric family of probability measures” is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. In case L2derivSymm is missing, it is filled with an object of class FunSymmList with entries NonSymmetric(). In case L2derivDistr is missing, it is computed via imageDistr. If L2derivDistrSymm is missing, it is set to an object of class DistrSymmList with entries NoSymmetry(). In case FisherInfo is missing, it is computed from L2deriv using E.