86,529 research outputs found
Asymptotic properties of the Bernstein density copula for dependent data
No full textCopulas 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
No full textThis 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
A resultant matrix for scaled Bernstein polynomials
No full textAbstractThe established theory of the resultant of two polynomials assumes that they are expressed in the power (monomial) basis, and a basis transformation is therefore necessary if the resultant of two Bernstein polynomials is required. In this paper, a resultant matrix for two scaled Bernstein polynomials (polynomials of degree n whose basis functions are (1−x)n−ixi,i=0,…,n) is constructed. In particular, a companion matrix M for a scaled Bernstein polynomial r(x) is developed, and this is used to form a resultant matrix s(M), where s(x) is a scaled Bernstein polynomial
On rates of convergence for posterior distributions in infinite-dimensional models
No full textThis paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of convergence for models including the mixture of Dirichlet process model and the random Bernstein polynomial model
Bernstein-Durrmeyer type operators
No full textRésuméWe study here a new kind of modified Bernstein polynomial operators on L1(0, 1) introduced by J. L. Durrmeyer in [4]. We define for f integrable on [0, 1] the modified Bernstein polynomial Mn f: Mnf(x) = (n + 1) ∑nk = oPnk(x)∝10 Pnk(t) f(t) dt. If the derivative dr fdxr with r ⩾ 0 is continuous on [0, 1], drdxrMn f converge uniformly on [0,1] and supxϵ[0,1] ¦Mn f(x) − f(x)¦ ⩽ 2ωf(1/trn) if ωf is the modulus of continuity of f. If f is in Sobolev space Wl,p(0, 1) with l ⩾ 0, p ⩾ 1, Mn f converge to f in wl,p(0, 1)
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Applying the ideas of Bernstein in the context of in-company management education
No full textIdeas drawn from the sociology of education have had surprisingly little impact on debates on organizational learning. This article takes ideas drawn from the sociology of education and applies them to a subset of organizational learning, the rapidly growing in company management programmes supplied by higher education institutions. It is argued that such programmes are often populated by participants who traditionally might not have engaged in higher education, making the explanatory frameworks of Bourdieu and Bernstein (with their central focus on education and class) relevant. An application of the concepts of Bernstein points to a need to make the notion of `relevance' in education problematic and to reasons why some participants might find the realization of a competent performance difficult
Extrapolation Properties of Multivariate Bernstein Polynomials
No full textWe consider some connections between the classical sequence of Bernstein polynomials and the Taylor expansion at the point 0 of a C^∞ function f defined on a convex open subset Ω⊂R^d containing the d-dimensional simplex S^d of R^d. Under general assumptions, we obtain that the sequence of Bernstein polynomials converges to the Taylor expansion and hence to the function f together with derivatives of every order not only on S^d but also on the whole Ω. This result yields extrapolation properties of the classical Bernstein operators and their derivatives. An extension of the Voronovskaja’s formula is also stated
A refinement of an inequality of S. Bernstein
No full textAbstractLet P(z) be a polynomial of degree n and P′(z) its derivative. Using a recently developed interpolation formula, we obtain certain interesting refinements of the well-known inequalities of S. Bernstein and M. Riesz for polynomials. Given P(1) = 0, the problem of estimating ¦P(r)¦, with 0 ⩽ r < 1, is also taken up. Finally we present a sharp lower bound concerning the maximum of ¦P′(z)¦ on ¦z¦ = 1
Weighted Fractional Bernstein'\''s inequalities and their applications
No full textThis paper studies the following weighted, fractional Bernstein inequality for spherical polynomials on \sph : \begin{equation}\label{4-1-TD-ab} \|(-\Delta_0)^{r/2} f\|_{p,w}\leq C_w n^{r} \|f\|_{p,w}, \ \ \forall f\in \Pi_n^d, \end{equation} where denotes the space of all spherical polynomials of degree at most on \sph , and is the fractional Laplacian-Beltrami operator on \sph . A new class of doubling weights with conditions weaker than the is introduced, and used to fully characterize those doubling weights on \sph for which the weighted Bernstein inequality \eqref{4-1-TD-ab} holds for some and all . In the unweighted case, it is shown that if is not an even integer, then \eqref{4-1-TD-ab} with holds if and only if r>(d-1)(\f 1p-1) . As applications, we show that any function f\in L_p(\sph) with can be approximated by the de la Vallée Poussin means of a Fourier-Laplace series, and establish a sharp Sobolev type Embedding theorem for the weighted Besov spaces with respect to general doubling weights
Postcard Written by Robert Bernstein to the Bryant College Service Club Dated April 8, 1943
No full text[Transcription begins]POST CARD
Pvt. Robert BernsteinA.A.F.T.T.C.Sq. 14 Flt. C.901st T. G., B.T.C. #9Miami Beach, Florida
April 8, 1943 [Postmark date]
Bryant Service ClubBryant College1 Young Orchard Ave.Providence, R. I.
U. S. ARMY AIR FORCES
Dear Bryant:
I\u27m having a swell time down here in Florida as much as I see it as the Army keeps me pretty busy. I\u27m stationed at the Basic Training Center of the Army Air Corp Technical Training Corp. It\u27s the strictest basic training center in the country but I like it a lot! Would you write me the names & addresses that you know of of the boys that left with the E.R.C.
Sincerely--Bob Bernstein[Transcription ends
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