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Statistical inference on nonparametric regression model with approximation of Fourier series function: Estimation and hypothesis testing. [PDF]

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Ramli M, Budiantara IN, Ratnasari V.
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Multivariate simultaneous approximation

Constructive Approximation, 2002
Using convolution techniques, the Fourier transform, and complex analysis, theorems of Jackson type are given, for the simultaneous approximation of a function of class \(C^m\) and its partial derivatives, by a polynomial and the corresponding partial derivatives.
BAGBY T., BOS, LEONARD PETER, LEVENBERG L.   +2 more
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Simultaneous Polynomial Approximation

SIAM Journal on Mathematical Analysis, 1993
The authors prove the approximation theorem on simultaneous approximation of \(f\in C^ s[- 1,1]\) and its derivatives of order \(j\), \(0\leq j\leq s\), by polynomials of degree \(n\) and their derivatives which has filled the gap between Timan-Trigub's type theorem and the classical norm estimate of the Jackson type.
Ditzian, Z., Jiang, Dechang, Leviatan, D.   +2 more
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Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
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Simultaneous Diophantine Approximation

Canadian Journal of Mathematics, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
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Suitable Norms for Simultaneous Approximation

Acta Mathematica Hungarica, 1997
The most common way to study simultaneous approximation of two points \(x,y\) of a normed linear space \(E\) from a subset \(M\) of \(E\), is to consider a suitable norm in \(E\times E\) (for instance, \(\| (u,v)\| =\sup(\| u\| ,\| v\|)\), \(\| (u,v)\| =\| u\| +\| v\|)\) and to reduce this problem to the ordinary approximation of the single point \((x ...
Benítez, Carlos, Fernández, Manuel, Soriano, María L.   +2 more
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On simultaneous approximation

Numerical Functional Analysis and Optimization, 1998
In this exposition, we investigate in an extended framework the problem of simultaneous best approximation. Refinement of a formula for the subdifferential of restricted radius of a p-bounded set leads us to explore some interesting results on strong uniqueness of simultaneous best approximants. In particular, we also.
LAURENT, PJ, PAI, D
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Simultaneous asymptotic Diophantine approximations

Mathematika, 1967
Let θ 1 , …, θ k be k real numbers. Suppose ψ( t ) is a positive decreasing function of the positive variable t . Define λ( N ), for all positive integers N , to be the number of solutions in integers p 1 …, p k , q of the inequalities ...
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ON SIMULTANEOUS PADÉ APPROXIMANTS

Mathematics of the USSR-Sbornik, 1982
A rather large class of systems of functions is investigated in connection with the simultaneous Pade approximants (normality, perfectness, problems of uniform convergence).Bibliography: 20 titles.
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Simultaneous Approximation and Algebraic Independence

The Ramanujan Journal, 1997
Rappelons la notion de mesure d'approximation simultanée (MAS): soit \(\theta= (\theta_1,\dots,\theta_n)\in \mathbb{C}^n\); une application \(\varphi: \mathbb{N}\times [0,+\infty[\to [0,+\infty]\) est une MAS pour \(\theta\) si il existe \(D_0\in\mathbb{N}\) et \(h_0\geq 1\) tels que, pour tout entier \(D\geq D_0\), tout nombre réel \(h\geq h_0\) et ...
Roy, Damien, Waldschmidt, Michel
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