16 results
Search Results
2. Empirical Likelihood Inference for Functional Coefficient ARCH-M Model.
- Author
-
Zhao, Hai Qing, Li, Yuan, and Zhao, Yan Meng
- Subjects
INFERENTIAL statistics ,ESTIMATION theory ,CHI-squared test ,CONFIDENCE regions (Mathematics) ,LIKELIHOOD ratio tests ,APPROXIMATION theory - Abstract
Empirical likelihood inference for parametric and nonparametric parts in functional coefficient ARCH-M models is investigated in this paper. Firstly, the kernel smoothing technique is used to estimate coefficient function δ(x). In this way we obtain an estimated function with parameter β. Secondly, the empirical likelihood method is developed to estimate the parameter β. An estimated empirical log-likelohood ratio is proved to be asymptotically standard chi-squred, and the maximum empirical likelihood estimation (MELE) for β is shown to be asymptotically normal. Finally, based on the MELE of β, the empirical likelihood approach is again applied to reestimate the nonparametric part δ(x). The empirical log-likelohood ratio for δ(x) is proved to be also asymptotically standard chi-squred. Simulation study shows that the proposed method works better than the normal approximation method in terms of average areas of confidence regions for β, and the empirical likelihood confidence belt for δ(x) performs well. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
3. Radial Operators on the Weighted Bergman Spaces over the Polydisk.
- Author
-
Li, Ran and Lu, Yu Feng
- Subjects
TOEPLITZ operators ,BERGMAN spaces ,APPROXIMATION theory ,MATHEMATICAL functions ,MATHEMATICS theorems - Abstract
In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the (m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its (0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its (m, λ)-Berezin transform is a separately radial function. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
4. Two classes of operators with irreducibility and the small and compact perturbations of them.
- Author
-
Zhang, Yun and Lin, Li
- Subjects
COMPACT operators ,PERTURBATION theory ,BANACH spaces ,LINEAR operators ,APPROXIMATION theory ,MATHEMATICAL analysis - Abstract
This paper gives the concepts of finite dimensional irreducible operators ((FDI) operators) and infinite dimensional irreducible operators ((IDI) operators). Discusses the relationships of (FDI) operators, (IDI) operators and strongly irreducible operators ((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an (FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in (ΣFDI)( X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in (ΣFDI)( X) with respect to the norm topology on a Banach space X with a Schauder basis, where (ΣFDI)( X):= { T ∈ B( X): T = Σ ⊕ T, T ∈ (FDI), k ∈ ℕ}. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
5. The Lp,q-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces Lp,q(ℝd+1).
- Author
-
Li, Rui, Liu, Bei, Liu, Rui, and Zhang, Qing Yue
- Subjects
RADON integrals ,APPROXIMATION theory ,MATHEMATICAL formulas ,MATHEMATICAL convolutions ,EQUATIONS - Abstract
The stability is an expected property for functions, which is widely considered in the study of approximation theory and wavelet analysis. In this paper, we consider the L
p,q -stability of the shifts of finitely many functions in mixed Lebesgue spaces Lp,q (ℝd+1 ). We first show that the shifts ϕ(· − k) (k ∈ ℤd+1 ) are Lp,q -stable if and only if for any ξ ∈ ℝd+1 , ∑k∈Zd+1|ϕ^(ξ+2πk)|2>0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L p,q (ℝd+1 ) to be Lp,q -stable which improves some known results. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
6. On the L-consistency of wavelet estimators.
- Author
-
Liu, You and Xu, Jun
- Subjects
WAVELETS (Mathematics) ,APPROXIMATION theory ,STATISTICAL sampling ,DENSITY functionals ,MONOTONIC functions - Abstract
This paper deals with the L-consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the L-consistency of wavelet estimators for independent and identically distributed random vectors in R. Then a similar result is obtained for negatively associated samples under the additional assumptions d = 1 and the monotonicity of the weight function. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. The finite-dimensional decomposition property in non-Archimedean Banach spaces.
- Author
-
Kubzdela, Albert and Perez-Garcia, Cristina
- Subjects
BANACH spaces ,APPROXIMATION theory ,MATHEMATICAL sequences ,MATHEMATICAL decomposition ,PROBLEM solving ,ORTHOGONAL systems - Abstract
A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property (OFDDP) if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces. This property has an influence in the non-Archimedean Grothendieck's approximation theory, where an open problem is the following: Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E. Does D have the OFDDP? In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP. Next we prove that, however, for certain classes of Banach spaces of countable type, the OFDDP is preserved by taking finite-codimensional subspaces. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
8. Dunkl's theory and best approximation by entire functions of exponential type in L-metric with power weight.
- Author
-
Liu, Yong and Song, Chun
- Subjects
APPROXIMATION theory ,MATHEMATICAL functions ,EXPONENTIAL functions ,MATHEMATICAL inequalities ,SUBSPACES (Mathematics) ,REFLECTION groups - Abstract
In this paper, we study the sharp Jackson inequality for the best approximation of f ∈ L(ℝ) by a subspace E( σ) ( SE( σ)), which is a subspace of entire functions of exponential type (spherical exponential type) at most σ. Here L(ℝ) denotes the space of all d-variate functions f endowed with the L-norm with the weight $v_\kappa (x) = \prod\nolimits_{\xi \in R_ + } {|(\xi ,x)|^{2\kappa (\xi )} } $, which is defined by a positive subsystem R of a finite root system R ⊂ ℝ and a function κ( ξ): R → ℝ invariant under the reflection group G( R) generated by R. In the case G( R) = ℤ, we get some exact results. Moreover, the deviation of best approximation by the subspace E( σ) ( SE( σ)) of some class of the smooth functions in the space L(ℝ) is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
9. The Lp,q-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces Lp,q(ℝd+1).
- Author
-
Li, Rui, Liu, Bei, Liu, Rui, and Zhang, Qing Yue
- Subjects
- *
RADON integrals , *APPROXIMATION theory , *MATHEMATICAL formulas , *MATHEMATICAL convolutions , *EQUATIONS - Abstract
The stability is an expected property for functions, which is widely considered in the study of approximation theory and wavelet analysis. In this paper, we consider the Lp,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(ℝd+1). We first show that the shifts ϕ(· − k) (k ∈ ℤd+1) are Lp,q-stable if and only if for any ξ ∈ ℝd+1, ∑k∈Zd+1|ϕ^(ξ+2πk)|2>0
. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(ℝd+1) to be Lp,q-stable which improves some known results. [ABSTRACT FROM AUTHOR] - Published
- 2018
- Full Text
- View/download PDF
10. The optimal constant in Hardy-type inequalities.
- Author
-
Chen, Mu-Fa
- Subjects
MATHEMATICAL constants ,MATHEMATICAL inequalities ,PARAMETER estimation ,APPROXIMATION theory ,FINITE fields - Abstract
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
11. Modelling, Analysis and Computation in Plasticity.
- Author
-
Reddy, B. Daya
- Subjects
NUMERICAL solutions to partial differential equations ,ALGORITHMS ,MATHEMATICAL inequalities ,MATERIAL plasticity ,APPROXIMATION theory ,STOCHASTIC convergence - Abstract
The typical problem in the mechanics of deformable solids comprises a mathematical model in the form of systems of partial differential equations or inequalities. Subsequent investigations are then concerned with analysis of the model to determine its well-posedness, followed by the development and implementation of algorithms to obtain approximate solutions to problems that are generally intractable in closed form. These processes of modelling, analysis, and computation are discussed with a focus on the behaviour of elastic-plastic bodies; these are materials which exhibit path-dependence and irreversibility in their behaviour. The resulting variational problem is an inequality that is not of standard elliptic or parabolic type. Properties of this formulation are reviewed, as are the conditions under which fully discrete approximations converge. A solution algorithm, motivated by the predictor-corrector algorithms that are common in elastoplastic problems, is presented and its convergence properties summarized. An important extension of the conventional theory is that of straingradient plasticity, in which gradients of the plastic strain appear in the formulation, and which includes a length scale not present in the conventional theory. Some recent results for strain-gradient plasticity are presented, and the work concludes with a brief description of current investigations. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
12. Semi-stable extensions over 1-dimensional bases.
- Author
-
Kollár, János, Nicaise, Johannes, and Xu, Chen
- Subjects
LAURENT series ,CALABI-Yau manifolds ,APPROXIMATION theory ,RIEMANN surfaces ,GALOIS modules (Algebra) - Abstract
Given a family of Calabi-Yau varieties over the punctured disc or over the field of Laurent series, we show that, after a finite base change, the family can be extended across the origin while keeping the canonical class trivial. More generally, we prove similar extension results for families whose log-canonical class is semi-ample. We use these to show that the Berkovich and essential skeleta agree for smooth varieties over ℂ(( t)) with semi-ample canonical class. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
13. Existence, uniqueness and approximation for L solutions of reflected BSDEs with generators of one-sided Osgood type.
- Author
-
Fan, Sheng
- Subjects
STOCHASTIC differential equations ,UNIQUENESS (Mathematics) ,APPROXIMATION theory ,LINEAR algebra ,GROWTH curves (Statistics) - Abstract
We prove several existence and uniqueness results for L ( p > 1) solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
14. The approximation properties determined by operator ideals.
- Author
-
Chen, Dong and Li, Lei
- Subjects
OPERATOR ideals ,APPROXIMATION theory ,BANACH algebras ,DUALITY theory (Mathematics) ,MATHEMATICAL analysis - Abstract
We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal A, that is, a Banach space X has the approximation property with respect to A whenever X* has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
15. Near convexity, near smoothness and approximative compactness of half spaces in Banach spaces.
- Author
-
Zhang, Zi, Zhou, Yu, and Liu, Chun
- Subjects
CONVEX domains ,BANACH spaces ,ASPLUND spaces ,APPROXIMATION theory ,DUALITY theory (Mathematics) - Abstract
The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
16. Conditional log-Laplace functional for a class of branching processes in random environments.
- Author
-
Wang, Hao
- Subjects
LAPLACE'S equation ,FUNCTIONAL analysis ,BRANCHING processes ,SET theory ,MATHEMATICAL decomposition ,APPROXIMATION theory - Abstract
A conditional log-Laplace functional (CLLF) for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments. CLLF will play an important role in the investigation of branching processes and superprocesses with interaction. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.