Semiparametric Estimation in Models of First-Price, Sealed-Bid Auctions with Affiliation

Within the affiliated private-values paradigm, we develop a tractable empirical model of equilibrium behaviour at first-price, sealed-bid auctions. The model is non-parametrically identified, but the rate of convergence in estimation is slow when the number of bidders is even moderately large, so we develop a semiparametric estimation strategy, focusing on the Archimedean family of copulae and implementing this framework using particular members--the Clayton, Frank, and Gumbel copulae. We apply our framework to data from low-price, sealed-bid auctions used by the Michigan Department of Transportation to procure road-resurfacing services, rejecting the hypothesis of independence and finding significant (and high) affiliation in cost signals.first-price, sealed-bid auctions, copulae, affiliation

A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging

Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging modalities such as hyper-spectral imaging, depth mapping, 3D profiling. However, the single-pixel technique requires sequential measurements resulting in a trade-off between spatial resolution and acquisition time, limiting real-time video applications to relatively low resolutions. Compressed sensing techniques can be used to improve this trade-off. However, in this low resolution regime, conventional compressed sensing techniques have limited impact due to lack of sparsity in the datasets. Here we present an alternative compressed sensing method in which we optimize the measurement order of the Hadamard basis, such that at discretized increments we obtain complete sampling for different spatial resolutions. In addition, this method uses deterministic acquisition, rather than the randomized sampling used in conventional compressed sensing. This so-called ‘Russian Dolls’ ordering also benefits from minimal computational overhead for image reconstruction. We find that this compressive approach performs as well as other compressive sensing techniques with greatly simplified post processing, resulting in significantly faster image reconstruction. Therefore, the proposed method may be useful for single-pixel imaging in the low resolution, high-frame rate regime, or video-rate acquisition

Geometric, Variational Integrators for Computer Animation

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details