Abstract
In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.
Highlights
A coordinate-free approach in finite populations was introduced by [1] as an alternative to the Gauss-Markov set up, used with the purpose of predicting linear functions
The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix
We extended this result assuming any known covariance matrix
Summary
A coordinate-free approach in finite populations was introduced by [1] as an alternative to the Gauss-Markov set up, used with the purpose of predicting linear functions. The Gauss-Markov approach is characterized by a dependence on a particular basis matrix, but in the coordinate-free language, we need only to describe a parametric subspace of IR N , where N is the size of the finite population. Our main objective is predicting ′Y , a linear combination of the elements of Y With this purpose, a sample of n observations is drawn of the population and the values of yi in Y become known for the sample elements. We extended the result, obtaining the best linear unbiased predictor of ′Y in the model (1.1) and this was the main contribution of the paper.
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