Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.Publicad

Power comparison among tests for fractional unit roots

This article compares the asymptotic power properties of the Wald, the Lagrange Multiplier and the Likelihood Ratio test for fractional unit roots. The paper shows that there is an asymptotic inequality between the three tests that holds under fixed alternatives.Publicad

Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991, 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first order asymptotic properties of the proposed tests are not affected by the pre-estimation of short or long memory parameter

A simple and general test for white noise

This article considers testing that a time series is uncorrelated when it possibly exhibits some form of dependence. Contrary to the currently employed tests that require selecting arbitrary user-chosen numbers to compute the associated tests statistics, we consider a test statistic that is very simple to use because it does not require any user chosen number and because its asymptotic null distribution is standard under general weak dependent conditions, and hence, asymptotic critical values are readily available. We consider the case of testing that the raw data is white noise, and also consider the case of applying the test to the residuals of an ARMA model. Finally, we also study finite sample performance

A simple test for normality for time series

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its simplicity, because it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.Publicad

Session 3-2-F: A Game-Theoretic Analysis of Baccara Chemin de Fer

Baccara chemin de fer — review of main contributions Baccara was first mentioned in print by Van Tenac in 1847. It was analyzed by Dormoy in 1872 and Bertrand in 1889. Borel called Bertrand’s study “extremely incomplete,” but it motivated Borel to develop game theory in the 1920s. Von Neumann planned to study baccara after proving the minimax theorem in 1928, but he didn’t. The first game-theoretic solution was by Kemeny and Snell in 1957. In 1964, Foster gave a solution based on a new algorithm, unaware of the Kemeny–Snell solution. A solution under more realistic assumptions was found by Downton and Lockwood in 1975 using Foster’s algorithm. Based on the extensive form of the game, the Kemeny–Snell solution was rederived by Deloche and Oguer in 2007

Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications

We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply. For special cases of the weights, the resulting variational problem is known to be equivalent to the fractional Poisson problem. The trace space for the weighted Sobolev space is identified to be embedded in a weighted $L^2$ space. We propose a finite element scheme to solve the Euler-Lagrange equations, and for the image denoising application we propose an algorithm to identify the unknown weights. The approach is illustrated on several test problems and it yields better results when compared to the existing total variation techniques

Nonlinear Hebbian learning as a unifying principle in receptive field formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely Nonlinear Hebbian Learning. When Nonlinear Hebbian Learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities

Center of Mass and spin for isolated sources of gravitational radiation

We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their Newtonian counterparts, though only variables at the null boundary of an asymptotically flat spacetime are used for their definition. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. The results are then compared to other approaches. In particular one obtains unexpected similarities as well as some differences with results obtained in the Post Newtonian literature . These equations of motion should be useful when describing the radiation emitted by compact sources such as coalescing binaries capable of producing gravitational kicks, supernovas, or scattering of compact objects.Comment: 16 pages. Accepted for publication in Phys. Rev.