Nothing
# Copyright (C) 2017 Markus Baaske. All Rights Reserved.
# This code is published under the GPL (>=3).
#
# File: qle-package.R
# Date: 27/10/2017
# Author: Markus Baaske
#
# General description of the package and data sets
#' Simulation-Based Quasi-Likelihood Estimation
#'
#' We provide a method for parameter estimation of parametric statistical models which can be at least
#' simulated and where standard methods, such as maximum likelihood, least squares or Bayesian
#' algorithms (including MCMC) are not applicable. We follow the \emph{quasi-likelihood} theory [3]
#' to estimate the unknown model parameter by finding a root of the so-called \dfn{quasi-score} estimating
#' function. For an overview of our method and further in-depth examples please see the vignette.
#'
#' The basic idea is to transform the general parameter estimation problem into a global (black box) optimization problem
#' (see [1]) with an expensive to evaluate objective function. This function can only be evaluated with substantial random
#' errors due to the Monte Carlo simulation approach of the statistical model and the interpolation error of the involved
#' approximating functions. The algorithm sequentially selects new evaluation points (which are the model parameters) for
#' simulating the statistical model and aims on efficiently exploring the parameter space towards a root of the quasi-score
#' vector as an estimate of the unknown model parameter by some weighted distance space-filling selection criteria of randomly
#' generated candidate points.
#'
#' The main estimation process can be started by the function \code{\link{qle}} where other functions like, for example,
#' \code{\link{qscoring}} or \code{\link{searchMinimizer}} search for a root or a local and global minimizer (without sampling new
#' candidates) of some monitor function to control the estimation procedure.
#'
#' @docType package
#' @name qle-package
#'
#' @references
#' \enumerate{
#' \item Baaske, M., Ballani, F., v.d. Boogaart,K.G. (2014). A quasi-likelihood
#' approach to parameter estimation for simulatable statistical models.
#' \emph{Image Analysis & Stereology}, 33(2):107-119.
#' \item Chiles, J. P., Delfiner, P. (1999). Geostatistics: modelling spatial uncertainty.
#' \emph{J. Wiley & Sons}, New York.
#' \item Heyde, C. C. (1997). Quasi-likelihood and its applications: a general approach
#' to optimal parameter estimation. \emph{Springer}
#' \item Kleijnen, J. P. C. & Beers, W. C. M. v. (2004). Application-driven sequential designs for simulation experiments:
#' Kriging metamodelling. \emph{Journal of the Operational Research Society}, 55(8), 876-883
#' \item Mardia, K. V. (1996). Kriging and splines with derivative information. \emph{Biometrika}, 83, 207-221
#' \item McFadden, D. (1989). A Method of Simulated Moments for Estimation of Discrete Response
#' Models without Numerical Integration. \emph{Econometrica}, 57(5), 995-1026.
#' \item Regis R. G., Shoemaker C. A. (2007). A stochastic radial basis function method for the global
#' optimization of expensive functions. \emph{INFORMS Journal on Computing}, 19(4), 497-509.
#' \item Wackernagel, H. (2003). Multivariate geostatistics. \emph{Springer}, Berlin.
#' \item Zimmermann, D. L. (1989). Computationally efficient restricted maximum likelihood estimation
#' of generalized covariance functions. \emph{Math. Geol.}. 21, 655-672
#' \item Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall, New York.
#' }
#'
#'
NULL
#' A normal model
#'
#' A statistical model of random numbers
#'
#' This is a pedagogic example of a simulated data set for quasi-likelihood estimation using
#' normally distributed random numbers. The model outcome is a vector of summary statistics, that is,
#' simply the median and mean average deviation of \code{n=10} random numbers, which is evaluated at the
#' model parameter \eqn{\theta=(\mu,\sigma)} with mean \eqn{\mu} and standard deviation \eqn{\sigma} as
#' the parameters of the normal distribution. We estimate the model parameter given a specific
#' "observation" of those summary statistics. Clearly, maximum likelihood estimation would be the
#' method of first choice if we had a real sample of observations. However, this example is used to demonstrate
#' the basic workflow of estimating the model parameter. We use this model as a standard example in the package
#' documentation.
#'
#' @docType data
#' @keywords datasets
#' @name qsd
#' @usage data(normal)
#' @format A list object named `\code{qsd}` of class \code{\link{QLmodel}} with additional elements
#' \itemize{
#' \item{simfn}{ simulation function }
#' \item{sim}{ simulation results at design points, class `\code{simQL}`}
#' \item{OPT}{ result from call to estimation function \code{qle}}
#' \item{QS}{ quasi-scoring iteration results after initial approximation}
#' }
#' @author M. Baaske
NULL
#' QLE estimation results of the normal model
#'
#' The results of estimating the parameters of the normal model by Quasi-likelihood.
#'
#' @docType data
#' @keywords datasets
#' @name OPT
#' @usage data(qleresult)
#' @format A list named `\code{OPT}` of class \code{\link{qle}}, see function \code{\link{qle}}
#' @author M. Baaske
NULL
#' QLE estimation results of M/M/1 queue
#'
#' The results of estimating the parameter of M/M/1 queue by Quasi-likelihood.
#'
#' @docType data
#' @keywords datasets
#' @name mm1q
#' @usage data(mm1q)
#' @format A list named `\code{mm1q}` with elements
#' \itemize{
#' \item{qsd}{ initial quasi-likelihood approximation model}
#' \item{OPT}{ the results of estimation by \code{\link{qle}}}
#' \item{Stest}{ score test results }
#' \item{OPTS}{ results from simulation study, see the vignette}
#' \item{Stest0}{ Score test after estimating the model parameter }
#' \item{tet0}{ original parameter value}
#' \item{obs0}{ generated observed statistics for simulation study}
#' }
#' @author M. Baaske
NULL
#' Matern cluster process data
#'
#' A data set of quasi-likelihood estimation results of estimating the parameters of a Matern cluster
#' point process model. In the vignette we apply our method to the `\code{redwood}` data set from the
#' package \code{spatstat}.
#'
#' @docType data
#' @keywords datasets
#' @name matclust
#' @usage data(matclust)
#' @format A list object named `\code{matclust}` which consists of
#' \itemize{
#' \item{qsd}{ initial quasi-likelihood approximation model}
#' \item{OPT}{ the results of estimation by \code{\link{qle}}}
#' \item{Stest}{ score test results }
#' }
#'
#' @author M. Baaske
NULL
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.