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Articles 1 - 7 of 7
Full-Text Articles in Entire DC Network
Applications And Algorithms For Least Trimmed Sum Of Absolute Deviations Regression, Douglas M. Hawkins, David Olive
Applications And Algorithms For Least Trimmed Sum Of Absolute Deviations Regression, Douglas M. Hawkins, David Olive
Articles and Preprints
High breakdown estimation (HBE) addresses the problem of getting reliable parameter estimates in the face of outliers that may be numerous and badly placed. In multiple regression, the standard HBE's have been those defined by the least median of squares (LMS) and the least trimmed squares (LTS) criteria. Both criteria lead to a partitioning of the data set's n cases into two “halves” – the covered “half” of cases are accommodated by the fit, while the uncovered “half”, which is intended to include any outliers, are ignored. In LMS, the criterion is the Chebyshev norm of the residuals of the …
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
We prove an existence theorem for solutions of stochastic functional differential equations under smooth constraints in Euclidean space. The initial states are semimartingales on a compact Riemannian manifold. It is shown that, under suitable regularity hypotheses on the coefficients, and given an initial semimartingale, a sfde on a compact manifold admits a unique solution living on the manifold for all time. We also discuss the Chen-Souriau regularity of the solution of the sfde in the initial process. The results are joint work with Remi Leandre.
The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed
The Stable Manifold Theorem For Stochastic Systems With Memory (Probability Seminar, Université Henri Poincaré Nancy 1), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
We state and prove a Local Stable Manifold Theorem for nonlinear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary solutions of sfde's. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques and interpolation arguments.
Small Extensions Of Witt Rings, Robert W. Fitzgerald
Small Extensions Of Witt Rings, Robert W. Fitzgerald
Articles and Preprints
We consider certain Witt ring extensions S of a noetherian Witt ring R obtained by adding one new generator. The conditions on the new generator are those known to hold when R is the Witt ring of a Field F, S is the Witt ring of a Field K and K/F is an odd degree extension. We show that if R is of elementary type then so is S.
Improved Feasible Solution Algorithms For High Breakdown Estimation, Douglas M. Hawkins, David J. Olive
Improved Feasible Solution Algorithms For High Breakdown Estimation, Douglas M. Hawkins, David J. Olive
Articles and Preprints
High breakdown estimation allows one to get reasonable estimates of the parameters from a sample of data even if that sample is contaminated by large numbers of awkwardly placed outliers. Two particular application areas in which this is of interest are multiple linear regression, and estimation of the location vector and scatter matrix of multivariate data. Standard high breakdown criteria for the regression problem are the least median of squares (LMS) and least trimmed squares (LTS); those for the multivariate location/scatter problem are the minimum volume ellipsoid (MVE) and minimum covariance determinant (MCD). All of these present daunting computational problems. …
Single-Change Circular Covering Designs, John P. Mcsorley
Single-Change Circular Covering Designs, John P. Mcsorley
Articles and Preprints
A single-change circular covering design (scccd) based on the set [v] = {1, . . . ,v} with block size k is an ordered collection of b blocks, B = {B1, . . . ,Bb}, each Bi ⊂ [v], which obey: (1) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [v] is covered by some Bi. The object is to minimize b for a fixed v and k. …
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …