437 research outputs found
Narcisse ou la mélancolie : lecture d'un sonnet de du Perron
No full textMathieu-Castellani Gisèle. Narcisse ou la mélancolie : lecture d'un sonnet de du Perron. In: Littérature, n°37, 1980. Le détail et son inconscient. pp. 25-36
Generalized Laplace inference in multiple change-points models
Get PDFUnder the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution, or a Bayes-type asymptotic distribution. We propose an inference method based on Highest Density Regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to better finite-sample performance.First author draf
Continuous record Laplace-based inference about the break date in structural change models
Get PDFBuilding upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method.A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise—lower mean absolute error (MAE) and lower root-mean squared error (RMSE)—than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.First author draf
Robert Morin : Preliminary Notes for a Western, 1990
No full textPerron delineates how Morin uses the conventions of the western genre and gives it a twist to speak of one's power - especially women's - against the codes and patriarchy of language. The author elaborates on the artist's strategies - such as the use of a female narrator playing both men and women characters - which create a form of distanciation that liberates the viewer. Biographical notes on artist and author
A linear spline maximum entropy method for Frobenius-Perron operators of multi-dimensional transformations
No full textA piecewise linear spline maximum entropy optimization method is described for the approximation of fixed densities of the Frobenius-Perron operator associated with higher-dimensional transformations. Convergence in 1-norm is proved and several examples with results are given.NSERC D
Perron-Frobenius theorem for nonnegative tensors
No full textWe generalize the Perron-Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.Mathematics, AppliedSCI(E)88ARTICLE2507-520
Linear convergence of the Collatz method for computing the Perron eigenpair of primitive dual number matrix
Get PDFVery recently, Qi and Cui extended the Perron-Frobenius theory to dual number
matrices with primitive and irreducible nonnegative standard parts and proved
that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz
method was also extended to find Perron eigenpair. Qi and Cui proposed two
conjectures. One is the k-order power of a dual number matrix tends to zero if
and only if the spectral radius of its standard part less than one, and another
is the linear convergence of the Collatz method. In this paper, we confirm
these conjectures and provide theoretical proof. The main contribution is to
show that the Collatz method R-linearly converges with an explicit rate.Comment: arXiv admin note: text overlap with arXiv:2306.16140 by other author
Nonlinear perron-probenius theory and dynamics of cone maps
No full textIn this paper several recent results concerning the dynamics of order preserving (sub) homogeneous maps on polyhedral cones are reviewed. These results were obtained by the author in collaboration with Marianne Akian, Stephane Gaubert, Roger Nussbaum, Michael Scheutzow and Colin Sparrow in [2], [13] and [15] and are new nonlinear extensions of the Perron-Frobenius theory
A piecewise linear spline maximum entropy method for Frobenius-Perron operators of multi-dimensional transformations
No full textIn 1976, Mathematician Tien-Yien Li published a solution to a conjecture by Ulam concerning a
finite approximation to the Frobenius-Perron operator. This accomplishment was a breakthrough
for the numerical approximation of the invariant densities that describe the statistical behaviour
of dynamical systems. Twenty years later, Jiu Ding and Aihui Zhou extended this method to
multi-dimensional transformations. Since then, several different methods have been developed to
approximate these invariant densities. Here, we present a piecewise linear spline maximum
entropy method for the approximation of invariant densities corresponding to multi-dimensional
transformations. Applications are considered and numerical results are explored
On the first and second order derivatives of the Perron vector
No full textAbstractIn a previous work [5] the authors developed formulas for the second order partial derivatives of the Perron root as a function of the matrix entries at an essentially nonnegative and irreducible matrix. These formulas, which involve the group generalized inverse of an associated M-matrix, were used to investigate the concavity and convexity of the Perron root as a function of the entries. The authors now combine the above results together with an approach taken in an earlier joint paper [6] of the second author with L. Elsner and C. Johnson, and they develop formulas for the second order derivatives of an appropriately normalized Perron vector with respect to the matrix entries, which again are given in terms the group generalized inverse of an associated M-matrix. Convexity properties of the Perron vector as a function of the entries of the matrix are then examined. In addition, formulas for the first derivative of the Perron vector resulting from different normalizations of this eigenvector are also given. A by-product of one of these formulas yields that the group generalized inverse of a singular and irreducible M-matrix can be diagonally scaled to a matrix which is entrywise column diagonally dominant
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