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Kinetic parameter estimation using PET is an important tool for in vivo quantification of physiological parameters in humans and animals. Iterative methods based on nonlinear weighted least squares criterion have been widely used to estimate kinetic parameters. Most of these methods do not guarantee to converge to the global optimum because the cost function is nonconvex and there may exist multiple local minima. In this paper, we propose to use the method of moments to estimate kinetic parameters. The method of moments results in a closed form solution for the kinetic parameters when volume of fraction is zero. We show that the method of moments yields reliable estimates that iterative methods may fail to provide depending on the initial conditions. The proposed method can be used alone, or to provide a good initial guess for iterative methods to improve convergence. The advantage of the method is demonstrated using both computer simulations and real dynamic PET data.