1,777,839 research outputs found
Circular Bernstein polynomial distributions
Get PDFThis paper introduces a new non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities which generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular data. It is shown that the trigonometric moments of the proposed circular Bernstein polynomial distribution can all be derived in closed form. We comment on how to fit the Bernstein polynomial density approximation to a sample of data and illustrate our approach with a real data example.Circular data, Non-parametric modeling, Bernstein polynomials
Asymptotic properties of the Bernstein density copula for dependent data
Get PDFCopulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α-mixing data using Bernstein polynomials. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality.nonparametric estimation, copula, Bernstein polynomial, α-mixing, asymptotic properties, boundary bias
Structured matrix methods for computations on Bernstein basis polynomials
Get PDFThis thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it is shown that structure preserving matrix methods yield excellent results.
With respect to greatest common divisor computations, the most difficult part is the computation of its degree, and several methods for its determination are presented.
These are based on the Sylvester resultant matrix, and it is shown that a new form of the Sylvester resultant matrix in the modified Bernstein basis yields the best results.
The B´ezout resultant matrix in the modified Bernstein basis is also considered, and it is shown that the results from it are inferior to those from the Sylvester resultant
matrix in the modified Bernstein basis
J.B. McNamara from Lina Bernstein, June 29, 1934-April 29, 1940
No full textLetters to J.B. McNamara from Lina Bernstein dated June 29, 1934 to April 29, 1940
bernstein-2017-productivity-and-diversity-2-18S
No full text<p>This is an 18S data set that is part of a larger project. Please visit our github repo for more information: <br>
https://github.com/pnnl/bernstein-2017-productivity-and-diversity-2</p>
bernstein-2017-productivity-and-diversity-2-16S
No full text<p>This is a 16S data set that is part of a larger project. Please visit our github repo for more information: <br>
https://github.com/pnnl/bernstein-2017-productivity-and-diversity-2</p>
The Bernstein-Von Mises Theorem in Semiparametric Competing Risks Models
Get PDFSemiparametric Bayesian models are nowadays a popular tool in survival analysis. An important area of research concerns the investigation of frequentist properties of these models. In this paper, a Bernstein-von Mises theorem is derived for semiparametric Bayesian models of competing risks data. The cause-specific hazard is taken as the product of the conditional probability of a failure type and the overall hazard rate. We model the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We show that the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions.Bayesian nonparametrics, Bernstein-von Mises theorem, beta process, competing risks, conditional probability of a failure type, semiparametric inference.
Bernstein family letters 1916-1918
No full textContains correspondence of Samuel Bernstein, a World War I draftee relating to his military training and personal matters. Also contains two letters from his brother, Charles Bernstein and two Yiddish letters to his fatherGift of Ralph Kolodn
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