200 research outputs found

    Optimal Estimation of Derivatives in Nonparametric Regression

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    Abstract We propose a simple framework for estimating derivatives without fitting the regression function in nonparametric regression. Unlike most existing methods that use the symmetric difference quotients, our method is constructed as a linear combination of observations. It is hence very flexible and applicable to both interior and boundary points, including most existing methods as special cases of ours. Within this framework, we define the variance-minimizing estimators for any order derivative of the regression function with a fixed bias-reduction level. For the equidistant design, we derive the asymptotic variance and bias of these estimators. We also show that our new method will, for the first time, achieve the asymptotically optimal convergence rate for difference-based estimators. Finally, we provide an effective criterion for selection of tuning parameters and demonstrate the usefulness of the proposed method through extensive simulation studies of the firstand second-order derivative estimators

    Predicting collective behaviour at the Hajj: place, space, and the process of cooperation

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    Around 2 million pilgrims attend the annual Hajj to Mecca and the holy places, which are subject to dense crowding. Both architecture and psychology can be part of disaster risk reduction in relation to crowding, since both can affect the nature of collective behaviour – particularly cooperation – among pilgrims. To date, collective behaviour at the Hajj has not been systematically investigated from a psychological perspective. We examined determinants of cooperation in the Grand Mosque and plaza during the pilgrimage. A questionnaire survey of 1194 pilgrims found that the Mosque was perceived by pilgrims as one of the most crowded ritual locations. Being in the plaza (compared to the Mosque) predicted the extent of cooperation, though crowd density did not. Shared social identity with the crowd explained more of the variance than both location and density. We examined some of the process underlying cooperation. The link between shared social identity and giving support to others was stronger in the plaza than in the Mosque, and suggests the role of place and space in modulating processes of cooperation in crowds. These findings have implications for disaster risk reduction and for applications such as computer simulations of crowds in pilgrimage locations

    Edge-texture feature based image forgery detection with cross dataset evaluation

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    A digital image is a rich medium of information. The development of user-friendly image editing tools has given rise to the need for image forensics. The existing methods for the investigation of the authenticity of an image perform well on a limited set of images or certain datasets but do not generalize well across different datasets. The challenge of image forensics is to detect the traces of tampering which distorts the texture patterns. A method for image forensics is proposed, which employs Discriminative robust local binary patterns (DRLBP) for encoding tampering traces and a support vector machine (SVM) for decision making. In addition, to validate the generalization of the proposed method, a new dataset is developed that consists of historic images, which have been tampered with by professionals. Extensive experiments were conducted using the developed dataset as well as the public domain benchmark datasets; the results demonstrate the robustness and effectiveness of the proposed method for tamper detection and validate its cross-dataset generalization. Based on the experimental results, directions are suggested that can improve dataset collection as well as algorithm evaluation protocols. More broadly, discussion in the community is stimulated regarding the very important, but largely neglected, issue of the capability of image forgery detection algorithms to generalize to new test data
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