765 research outputs found
Computational methods for estimation of parameters in hyperbolic systems
Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized
Comparisons of two quantile regression smoothers
The paper compares the small-sample properties of two non-parametric quantile
regression estimators. The first is based on constrained B-spline smoothing
(COBS) and the other is based on a variation and slight extension of a running
interval smoother, which apparently has not been studied via simulations. The
motivation for this paper stems from the Well Elderly 2 study, a portion of
which was aimed at understanding the association between the cortisol awakening
response and two measures of stress.
COBS indicated what appeared be an usual form of curvature. The modified
running interval smoother gave a strikingly different estimate, which raised
the issue of how it compares to COBS in terms of mean squared error and bias as
well as its ability to avoid a spurious indication of curvature. R functions
for applying the methods were used in conjunction with default settings for the
various optional arguments. The results indicate that the modified running
interval smoother has practical value. Manipulation of the optional arguments
might impact the relative merits of the two methods, but the extent to which
this is the case remains unknown.Comment: 18 pp, 5 figure
Discrete B-splines and subdivision techniques in compter-aided geometric design and computer graphics
Journal ArticleThe relevant theory of discrete 5-sphnes with associated new algorithms is extended to provide a framework for understanding and implementing general subdivision schemes for nonuniform B-splines. The new derived polygon corresponding to an arbitrary refinement of the knot vector for an existing .B-spline curve, including multiplicities, is shown to be formed by successive evaluations of the discrete B-spline defined by the original vertices, the original knot vector, and the new refined knot vector. Existing subdivision algorithms can be seen as proper special cases. General subdivision has widespread applications in computer-aided geometric design, computer graphics, and numerical analysis. The new algorithms resulting from the new theory lead to a unification of the display model, the analysis model, and other needed models into a single geometric model from which other necessary models are easily derived. New sample algorithms for interference calculation, contouring, surface rendering, and other important calculations are presented
Separated flow over bodies of revolution using an unsteady discrete-vorticity cross wake. Part 2: Computer program description
A method is developed to determine the flow field of a body of revolution in separated flow. The computer was used to integrate various solutions and solution properties of the sub-flow fields which made up the entire flow field without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the two-dimensional unsteady separated flow problem based upon an unsteady, discrete-vorticity wake. Data for the forces and moments on aerodynamic bodies at low speeds and high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data. In addition, three dimensional steady separated regions and wake vortex patterns are determined. The computer program developed to perform the numerical calculations is described
Generalized Additive Modeling For Multivariate Distributions
In this thesis, we develop tools to study the influence of predictors on multivariate distributions. We tackle the issue of conditional dependence modeling using generalized additive models, a natural extension of linear and generalized linear models allowing for smooth functions of the covariates. Compared to existing methods, the framework that we develop has two main advantages. First, it is completely flexible, in the sense that the dependence structure can vary with an arbitrary set of covariates in a parametric, nonparametric or semiparametric way. Second, it is both quick and numerically stable, which means that it is suitable for exploratory data analysis and stepwise model building. Starting from the bivariate case, we extend our framework to pair-copula constructions, and open new possibilities for further applied and methodological work. Our regression-like theory of the dependence, being built on conditional copulas and generalized additive models, is at the same time theoretically sound and practically useful
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