qle (version 0.18)

Subset of statistics: Optimal subset selection of statistics

Description

The function finds a subset of at most \(kmax <= p\) statistics, where p is the number of available statistics in the list `qsd$covT` (and at least of size equal to the length q of the parameter `theta`) and thus minimizes the expected estimation error of the parameter when this subset is used for estimation. Based on the eigenvalue decomposition of the variance-covariance matrix of the statistics this subset is chosen among all subsets of size at most equal to `kmax` or for which all proportional contributions to each parameter component are greater than or equal to `cumprop` whatever happens first.

Since both matrices depend on `theta` so does the chosen subset of statistics. However, using a list of parameters as `theta` returns a list of corresponding subsets. One can then easily choose the most frequent subset among all computed ones given either a sample of parameters distributed over the whole parameter space or an appropriate smaller region, where, e.g., the starting point is chosen from or the true model parameter is expected to lie in.

Usage

optStat(theta, qsd, kmax = p, cumprop = 1, ..., cl = NULL,
  verbose = FALSE)

Arguments

theta

list or matrix of points where to compute the criterion function and to choose `kmax` statistics given the QL model `qsd`

qsd

object of class QLmodel

kmax

number of statistics to be selectnred (q <= kmax <= p)

cumprop

numeric vector either of length one (then replicated) or equal to the length of `theta` which sets the proportions (0 < cumprop <= 1) of minimum overall contributions to each parameter component given the statistics

...

further arguments passed to quasiDeviance or mahalDist

cl

cluster object, NULL (default), of class MPIcluster, SOCKcluster, cluster

verbose

logical, TRUE for intermediate output

Value

A list which consists of

id

indices of corresponding statistics

names

names of statistics (if provided)

cumprop

cumulated proportions of contributions of selected statistics to each of the parameter components

sorted

list of statistics (for each parameter) sorted in decreasing order of proportional contributions to the quasi-information

Examples

# NOT RUN {
 data(normal)
 # must select all statistics and thus using the
 # full information since we only have to statistics available 
 optStat(c("mu"=2,"sigma"=1),qsd,kmax=2)[[1]]

# }