High Resolution (HR) methods are known to provide accurate frequency estimates for discrete spectra [1]. The Polynomial Amplitude Complex Exponentials (PACE) model was presented as the most general model tractable by HR methods. A subspace-based estimation scheme was recently proposed in [2], derived from the ESPRIT algorithm [3]. In [4], we focused on the performance of this estimator. We first presented some asymptotic expansions of the estimated parameters, obtained at the first order under the assumption of a high signal-to-noise ratio (SNR). Then the performance of the generalized ESPRIT algorithm for estimating the parameters of this model was analyzed in terms of bias and variance, and compared to the Cramér-Rao bounds. In this supporting document, we present the proofs of the theoretical results introduced in [4]. This document, written as a sequel of [4], is not intended to be read separately. It is organized as follows: section I is devoted to the perturbation analysis, then the performance of the estimators is analyzed in section II.