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#' Predict the warping parameters.
#'
#' This function predict the warping parameters, using the estimations of those parameters,
#' and fitting a linear mixed effect model on them.
#'
#' @param thetaObs A matrix (size: n * T) corresponding of the estimations of the warping parameters.
#' @param sigmaEpsilon A number, defining the variance of the noise in the linear mixed-
#' effect model fitted on the warping parameters.
#'
#' @return A list, with theta, a matrix of predicted warping parameters,
#' sigmaE the covariance of the random effects, and theta0 the mean.
#'
#'
predictionTheta = function(thetaObs,sigmaEpsilon){
## Initialization
thetaObs = t(thetaObs)
A = dim(thetaObs)
n = A[1]
T = A[2]
## Compute the prediction
theta0hat = apply(thetaObs,2, mean)
sigmaEhat = cov(thetaObs) - sigmaEpsilon * diag(1,T)
effetAlea = sigmaEhat %*% solve(cov(thetaObs)) %*% t(thetaObs)
result = list(theta = effetAlea, sigmaE = sigmaEhat, theta0 = theta0hat)
return(result)
}
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