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In contrast to the assumption of perfect observations by a number of developed methods for the analysis of nonstationary signals, missing observations do occur in practice which lead to performance degradation. We consider the parameter estimation problem of multicomponent polynomial phase signals (PPS) when there are randomly missing observations. The derivation shows that the Cramer-Rao bound for the missing observations case can be readily obtained from the result of perfect observations. Then, we propose an expectation-maximization-based method to estimate the PPS parameters. Simulation results show that the proposed method approaches the Cramer-Rao bound at moderate to high signal-to-noise ratios whilst standard techniques fail when there is a fair amount of missing observations.