  Prediction performance does not always reflect the estimation behaviour of a
method. High error in estimation may necessarily not result in high prediction
error, but can lead to an unreliable prediction if test data lie in a slightly
different subspace than the training data. In addition, high estimation error
often leads to unstable estimates, and consequently, the estimated effect of
predictors on the response can not have a valid interpretation. Many research
fields show more interest in the effect of predictor variables than actual
prediction performance. This study compares some newly-developed (envelope) and
well-established (PCR, PLS) estimation methods using simulated data with
specifically designed properties such as Multicollinearity in the predictor
variables, the correlation between multiple responses and the position of
principal components corresponding to predictors that are relevant for the
response. This study aims to give some insights into these methods and help the
researchers to understand and use them for further study. Here we have, not
surprisingly, found that no single method is superior to others, but each has
its strength for some specific nature of data. In addition, the newly developed
envelope method has shown impressive results in finding relevant information
from data using significantly fewer components than the other methods.
