fitSIRFk: Estimation of covariance parameters

In qle: Simulation-Based Quasi-Likelihood Estimation

Description

Fit a generalized covariance model to simulation data

Usage

fitSIRFk(qldata, set.var = TRUE, var.type = "wcholMean",
  var.opts = list(var.sim = 1e-06), intrinsic = FALSE, ...,
  control = list(), cl = NULL, pl = 0L, verbose = FALSE)

Arguments

qldata	object of class QLdata, a data frame from function setQLdata
set.var	logical vector of length one or equal to the number of covariance models; for values TRUE (default), set simulation variances as local nugget variances for the corresponding covariance model according to its index
var.type	name of variance matrix approximation type (see covarTx)
var.opts	list of arguments passed to setCovModel (only if 'var.type'="kriging" and ignored otherwise)
intrinsic	logical vector, FALSE (default), of length one or equal to the number of Cholesky decompositions of variance matrices; as default use an internal nugget variance estimate (see details) for kriging the variance matrix of the statistics
...	arguments passed to setCovModel
control	list of control parameters passed to nloptr for local minimization
cl	cluster object, NULL (default), of class "MPIcluster", "SOCKcluster", "cluster"
pl	integer, print level pl=0 (default)
verbose	if TRUE, show intermediate output

Details

The function contructs and estimates the parameters of the covariance models by the REML estimatino method for both kriging the sample means of the statistics and kriging the variance matrix of statistics unless 'var.type' equals "const" for the latter. The default covariance model is derived from a (self-similar) intrinsic random function, that is, the 'sirfk' function of order k (see, e.g. [1]) with k=1,2, for all statistics (including a default quadratic drift term k=2). The user can also define different covariance models for each statistic separately (see below). Other covariance models can be set by their name in the argument 'model' which is passed to the function setCovModel. Currently, kriging the variance matrix is done by the 'sirfk' model.

The argument 'var.opts' only sets the options for the covariance models for kriging the variance matrix if this is the users prefered type of approximation. Further optional arguments, e.g., 'var.sim' used only for the approximatino of the statistics, 'var.opts$var.sim' for kriging the variance matrix, specify the local vector of nugget values for each sample point depending on whether or not 'set.var' (which is only used for kriging the statistics) equals TRUE. Both arguments are passed to setCovModel and must be data frames of lengths (number of columns) corresponding to the number of covariance models of the statistics and, respectively, to the number of Cholesky decomposed terms in case of kriging the variance matrix. If 'set.var=TRUE' (default), then local nugget variances are estimated by the variance of the sample average of the simulated values of the statistics. Otherwise the values given in 'var.sim' are used as fixed 'nugget' variances and replicated to match the number of sample points.

The same applies in case of kriging the variance matrix. If 'intrinsic=TRUE', then local nugget variances for each of the variance-covariances of the statistics are estimated by a bootstrapping procedure. Otherwise the values given by 'var.opts$var.sim' (of length one or equal to the number of corresponding sample points) are used directly as local estimates (which then must exactly match the order of the Cholesky decomposed terms). A global nugget value can be estimated during the REML estimation which is the default option for both cases unless this parameter is excluded from the covariance parameter estimation (see setCovModel).

The default optimization algorithm for estimating the covariance parameters is mlsl followed by a final local search using NLOPT_LN_COBYLA. Note that in this case the estimated parameters may vary when starting the REML procedure several times since starting points are randomly chosen for mlsl. All options for optimization can be modified by the argument 'control'.

Note that the returned object can also be constructed manually and passed as an input argument to QLmodel in case the user prefers to set up each covariance model separately. In this case, first use setCovModel to construct the covariance model, then estimate the parameters by fitCov and pass a list of fitted covariance models to function QLmodel. The resulting object is the same as obtained by this function. Please see the function QLmodel for an example.

Value

A list of fitted covariance models for kriging the sample means of statistics named 'covT' and optionally the variance matrix of statistics, 'covL'. The object also stores the reml optimization parameters 'control'.

Author(s)

M. Baaske

See Also

setCovModel, fitCov, QLmodel

qle documentation built on May 2, 2019, 5:26 p.m.