23,128 research outputs found
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 â 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 Bertrandâs study âextremely incomplete,â 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 didnât.
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 KemenyâSnell solution.
A solution under more realistic assumptions was found by Downton and Lockwood in 1975 using Fosterâs algorithm.
Based on the extensive form of the game, the KemenyâSnell 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 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.
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