We present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods. In our approach, Kendall's definition of shape is used for feature extraction. Since the shape feature rests on a non-Euclidean manifold, we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait-based human recognition. The nonparametric model is based on dynamic time-warping. We suggest a modification of the dynamic time-warping algorithm to include the nature of the non-Euclidean space in which the shape deformations take place. We also show the efficacy of this algorithm by its application to gait-based human recognition. We exploit the shape deformations of a person's silhouette as a discriminating feature and provide recognition results using the nonparametric model. Our analysis leads to some interesting observations on the role of shape and kinematics in automated gait-based person authentication.