#' Wrapper for Anderson-Darling tests
#' 
#' A set of Anderson-Darling tests (Anderson and Darling, 1952) are applied as
#' proposed by Aitchison (Aichison, 1986).
#' 
#' First, the data is transformed using the \sQuote{ilr}-transformation.  After
#' applying this transformation
#' 
#' - all (D-1)-dimensional marginal, univariate distributions are tested using
#' the univariate Anderson-Darling test for normality.
#' 
#' - all 0.5 (D-1)(D-2)-dimensional bivariate angle distributions are tested
#' using the Anderson-Darling angle test for normality.
#' 
#' - the (D-1)-dimensional radius distribution is tested using the
#' Anderson-Darling radius test for normality.
#' 
#' @param x compositional data of class data.frame or matrix
#' @param alpha significance level
#' @param R Number of Monte Carlo simulations in order to provide p-values.
#' @param robustEst logical
#' @return \item{res }{ a list including each test result } \item{check }{
#' information about the rejection of the null hypothesis} \item{alpha}{ the
#' underlying significance level } \item{info}{ further information which is
#' used by the print and summary method. } \item{est}{ \dQuote{standard} for
#' standard estimation and \dQuote{robust} for robust estimation }
#' @author Matthias Templ and Karel Hron
#' @seealso \code{\link{adtest}}, \code{\link{isomLR}}
#' @references Anderson, T.W. and Darling, D.A. (1952) \emph{Asymptotic theory
#' of certain goodness-of-fit criteria based on stochastic processes} Annals of
#' Mathematical Statistics, \bold{23} 193-212.
#' 
#' Aitchison, J. (1986) \emph{The Statistical Analysis of Compositional Data}
#' Monographs on Statistics and Applied Probability. Chapman \& Hall Ltd.,
#' London (UK). 416p.
#' @keywords htest
#' @examples
#' 
#' data(machineOperators)
#' a <- adtestWrapper(machineOperators, R=50) # choose higher value of R
#' a
#' summary(a)
#' 
adtestWrapper=function(x,alpha=0.05,R=1000, robustEst=FALSE){
if(robustEst == TRUE ) robust <- "robust" else robust <- "standard"
z=isomLR(x)
n=ncol(z)
if(ncol(z)==1){
  res<-info<-list()
  res[[1]]=adtest(z,R,locscatt=robust)
  info[[1]]=paste(1)
  check<- logical(1)
}
if(ncol(z)==2){
  res<-info<-list()
  res[[1]]=adtest(z[,1],R,locscatt=robust)
  res[[2]]=adtest(z[,2],R,locscatt=robust) 
  res[[3]]=adtest(z,R,locscatt=robust)
  info[[1]]=paste(1)
  info[[2]]=paste(2)
  info[[3]]=paste(3)
  check <- logical(3)
}
if(ncol(z)>2){
  res<-info<-list()
  for(i in 1:ncol(z)){
    res[[i]]=adtest(z[,i],R,locscatt=robust)
    info[[i]]=paste(i)
  }
  index=1
  for(i in 1:(ncol(z)-1)){
    for(j in (i+1):ncol(z)){     
      res[[n+index]]=adtest(z[,c(i,j)],R,locscatt=robust)
      info[[n+index]]=paste(i,j,collapse=":")
      index=index+1
    }
  }
  res[[n+index]]=adtest(z,R,locscatt=robust)
  info[[n+index]]=paste("all")
  check <- logical(n+index)  
}

for(i in 1:length(check)){  
  check[i] <- ifelse(res[[i]]$p.value > alpha, TRUE, FALSE)
}
output=list(res=res, check=check, alpha=alpha, info=info, est=robust)
class(output)="adtestWrapper"
invisible(output)
}