Mixed Statistical Estimation in Constrained Principal Component Model

Abstract

There was found a serious problem in the statistical estimation if we don't reject a false hypothesis because of ignoring prior information about the estimator, constrained principal component model (CPCM) considered to be a general model for many constrained estimator, but this model do not important with the additional information about the error term that found in the restriction model. This paper seeks to find another face for the constrained principal component model that important with the variance of the error term that found in the restriction model and have a value dispute zero. This paper aims to introduce a generalized ordinary mixed estimator (GOME) using the CPCM which introduced by (Takane, 2014) and we try to find some special cases for this estimator which introduced earlier. The new estimator is more benefit for researchers in making decisions and depending on results that have more credible. We try to get the subset models and their constrained from the constrained principal component model; a model and a constrained model each of them have a variance term that have value despite zero, we also try to make a mixed estimator for each model and combined them to get the GOME and try to find the superiority of the new estimator.