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This paper studies the parameter estimation for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. We propose computationally efficient estimators based on the method of moments that are robust to model misspecification. We develop an analytical framework that enables closed-form representation of model parameters in terms of the moments and autocorrelations of observed underlying processes. Under moderate assumptions, which are typically much weaker than those for likelihood methods, we prove large-sample behaviors for our proposed estimators, including strong consistency and asymptotic normality. Our estimators obtain the canonical square-root convergence rate and are shown through numerical experiments to outperform likelihood-based methods.
We present a 3D reconstruction method using brightness and camera motion estimation for registering local colon structure in colonoscopy. The proposed method is based on reverse projection from 2D fold contours to 3D space, motion estimation from 3D reconstructed points between neighboring frames, and model registration to reconstruct the fold structure. On the synthetic colon, the average percentages of the reconstructed depth error and circumference error are about 14.2% and 15.2%, respectively. The accuracy is enough for the navigation and control in capsule robot. This work demonstrates that the proposed method is superior to the methods using single-frame-based brightness intensity.