# An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

It was recently proposed to encode the one-sided exponential source X into K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,K, are one-sided exponential and mutually independent given X [1], [2]. Moreover, it was shown that the optimal estimator Ŷ of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., Ŷ = maxY1,..., YK. In this paper, we show that the distribution of the resulting estimation error X - Ŷ , is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y1,...,YK.

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