Special PDE Seminar
Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
(Refreshments at 167 Angell St., 2 floor conference room right after seminar.) *Sponsored by the C. V. Starr Foundation Lectureships Fund |
Abstract: We consider nonparametric and semiparametric regression estimation for clustered data using estimating equations. The first half of the talk discusses the use of the kernel method for nonparametric regression with a single covariate. We show that it is generally the best strategy to ignore entirely the correlation structure within each cluster, and instead to pretend that all observations are independent. Correctly specifying the correlation structure in fact results in an asymptotically less efficient estimator. The second half of the talk extends nonparametric regression to semiparametric regression for clustered data where some additional covariates effects are modeled parametrically using the profile/kernel estimating equations. We show that correct specification of the correlation structure leads to inconsistent estimates of the finite dimensional parameteric parameters. Consistent estimates of both the parametric and nonparametric parameters require completely ignoring the within-cluster correlation. We apply the proposed methods to the analysis of the AIDS Costs and Services Utilization Survey. This is a joint work with Ray Carroll.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Brown Analysis Seminar
TURKEY TALK - Applied Mathematics Colloquium
Abstract: The speaker will discuss four questions selected from a number submitted to him by both faculty and students. After a ten minute discussion of each question by the speaker, there will be a five minute period for audience response.
Scientific Computing Seminar
Abstract: Hamilton-Jacobi equation arise in many areas of application, e.g. calculus of variations, control theory, differential games, image processing. Its generalized solutions are Lipschitz continuous, but may have discontinuous derivatives.
In this talk I will present the numerical solution of the Hamilton-Jacobi initial boundary value problem by the spectral/pseudospectral viscosity method. This method may be considered as a compromise between the vanishing viscosity approximation and the usual spectral/pseudospectral method.
I will prove that the numerical solution is formally spectral accurate and converges to the exact unique viscosity solution. I will also show some numerical simulations.
PDE Seminar
Department of Mathematics Colloquium
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