Limit Theorems for Random Fields with Singular Spectrum

Leonenko, Nikolai

doi:10.1007/978-94-011-4607-4

Cited by 153 publications

(178 citation statements)

References 0 publications

Supporting

Mentioning

172

Contrasting

Unclassified

Order By: Relevance

“…Assume that the resolution of unity (9) is adapted to Γ , as described in Definition 11. If we take a finite sum of this representation, which is a smooth function ϕ, its restriction to Γ admits a quarkonial representation (24). Therefore, by Lemma 14, Theorem 10 and (26) for our ϕ and τ = 1, by continuous extension, tr Γ g exists and…”

Section: 2mentioning

confidence: 90%

See 1 more Smart Citation

Spaces of generalized smoothness on h-sets and related Dirichlet forms

Knopova

Zähle

2006

Studia Math.

View full text Add to dashboard Cite

Abstract. The paper is devoted to spaces of generalized smoothness on so-called h-sets. First we find quarkonial representations of isotropic spaces of generalized smoothness on R n and on an h-set. Then we investigate representations of such spaces via differences, which are very helpful when we want to find an explicit representation of the domain of a Dirichlet form on h-sets. We prove that both representations are equivalent, and also find the domain of some time-changed Dirichlet form on an h-set.1. Introduction. The paper is devoted to Besov-type spaces on h-sets. Such sets were defined and studied in Edmunds and Triebel [5], [6]; see also Bricchi [3] and [4]. Our goal is to study more general spaces on such sets, and show how these results can be applied when we look for the domain of Dirichlet forms on an h-set, associated with restrictions of certain symmetric Lévy processes to this set.

show abstract

Section: 2mentioning

confidence: 90%

“…Then B σ * ,N pq (Γ ) ̺ is the collection of all functions g ∈ L 1 (Γ ) which can be represented as (24) g…”

Section: 2mentioning

confidence: 99%

Spaces of generalized smoothness on h-sets and related Dirichlet forms

Knopova

Zähle

2006

Studia Math.

View full text Add to dashboard Cite

show abstract

“…Below we provide some examples. Denote by Φ(·) the standard Gaussian distribution function and let U be the uniform Parametric regression models (1) with discrete or with continuous time and longmemory errors without constraints (2) are considered by Dobrushin and Major [5], Yajima [18], Künsch, Beran, and Hampel [10], Dahlhaus [4], and Leonenko [11] (also see the references therein). On the other hand, regression models (1) with independent or weakly dependent errors and constraints (2) are considered by Korkhin [2] and Knopov [1].…”

Section: Let η(T) = G(ε(t))mentioning

confidence: 99%

“…Taqqu [16] and Dobrushin and Major [5] proved the noncentral limit theorem that characterizes such models. The further asymptotic theory of least squares estimators for long-memory dependence models without constraints is due to Yajima [18], Künsch, Beran, and Hampel [10], Dahlhaus [4], Leonenko and Bensic [12], Leonenko [11], Ivanov and Leonenko [7]- [9].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic distributions of least squares estimators of the coefficients in the model of linear regression with nonlinear constraints and long-memory dependence

Moldavs'ka

2008

Theor. Probability and Math. Statist.

View full text Add to dashboard Cite

Abstract. We consider least squares estimators for linear regression models with long-memory dependence, continuous time, and nonlinear inequality constraints imposed on the parameter. We study the solution of the problem of minimization of the least squares functional in the linear regression with a given (long) radius of dependence and nonlinear inequality constraints imposed on the parameter. We prove that the solution being appropriately centered and normalized converges in distribution to the solution of the quadratic programming problem. The latter solution is non-Gaussian in contrast to known results for long-memory dependence without constraints for which an analogous transform of the solution of the minimization problem is asymptotically Gaussian in many typical cases.

show abstract

“…Priestley (1964), Rozanov (1967), Brillinger (1970), Rosenblatt (1985), Ivanov and Leonenko (1986), Žurbenko (1986), Heyde and Gay (1993), and Leonenko (1999), among others. The basic theory is a straightforward generalization from time series.…”

Section: Introductionmentioning

confidence: 99%

Automatic spectral density estimation for random fields on a lattice via bootstrap

Vidal-Sanz

2007

TEST

View full text Add to dashboard Cite

This paper considers the nonparametric estimation of spectral densities for second order stationary random fields on a d-dimensional lattice. I discuss some drawbacks of standard methods, and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. I prove uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.Keywords: Spatial data, spectral density, smoothing number, uniform asymptotic distribution, Bootstrap. AMS 2000 subject classifications:. Primary 62M30; secondary 62M15, 62G20 * A version of this paper is published in TEST, by Springer Verlag, DOI 10.1007/s11749-007-0059-5. I wish to thank Professor C. Velasco and two anonymous referees for their helpful comments and suggestions, and Professor P. M. Robinson for introducing me in the topic.

show abstract

Limit Theorems for Random Fields with Singular Spectrum

Cited by 153 publications

References 0 publications

Spaces of generalized smoothness on h-sets and related Dirichlet forms

Spaces of generalized smoothness on h-sets and related Dirichlet forms

Asymptotic distributions of least squares estimators of the coefficients in the model of linear regression with nonlinear constraints and long-memory dependence

Automatic spectral density estimation for random fields on a lattice via bootstrap

Contact Info

Product

Resources

About