Weak convergence of weighted additive functionals of long-range dependent fields

Alodat, Tareq; Olenko, Andriy

doi:10.1090/tpms/1044

Cited by 9 publications

(9 citation statements)

References 24 publications

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“…Therefore, it is important to obtain theoretical results about asymptotics for general types of observation windows. In this paper we extend results of Leonenko and Taufer (2006) and Alodat and Olenko (2017) under more general conditions. More precisely, we consider weighted functionals of random fields of the form…”

Section: Introductionsupporting

confidence: 64%

On asymptotics of discretized functionals of long-range dependent functional data

Alodat

Olenko

2020

Communications in Statistics - Theory and Methods

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The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given by these functionals. It is shown that in the discrete sampling case additive functionals have the same asymptotic distribution as the corresponding integral functionals for the continuous functional data case. These results are applied to obtain non-central limit theorems for weighted additive functionals of random fields. As the majority of known results concern the discrete sampling case the developed methodology helps in translating these results to functional data without deriving them again. Numerical studies suggest that the theoretical findings are valid for wider classes of long-range dependent data.

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Section: Introductionsupporting

confidence: 64%

On asymptotics of discretized functionals of long-range dependent functional data

Alodat

Olenko

2020

Communications in Statistics - Theory and Methods

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“…In the available literature, it is usually assumed as a matter of fact that the discretization error is negligible with respect to the estimation error. There are only few known results that rigorously prove it (see Alodat & Olenko, ; Ayache & Bertrand, ; Bardet & Bertrand, ; Leonenko & Taufer, ). We intend to devote another publication to investigating discretization errors.…”

Section: Simulation Studiesmentioning

confidence: 98%

Estimation of cyclic long‐memory parameters

Alomari

Ayache

Fradon

et al. 2019

Scandinavian J Statistics

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This paper studies cyclic long‐memory processes with Gegenbauer‐type spectral densities. For a semiparametric statistical model, new simultaneous estimates for singularity location and long‐memory parameters are proposed. This generalized filtered method‐of‐moments approach is based on general filter transforms that include wavelet transformations as a particular case. It is proved that the estimates are almost surely convergent to the true values of parameters. Solutions of the estimation equations are studied, and adjusted statistics are proposed. Monte‐Carlo study results are presented to confirm the theoretical findings.

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“…(iii) f (λ, θ) > 0, (λ, θ) ∈ R × Θ c . In the condition A 2 (ii) above θ (1) represents parameters of the kernel â in (4), while θ (2) represents parameters of LГқvy process.…”

Section: Settingmentioning

confidence: 99%

“…In the present publication continues-time model is considered. However, the results obtained can be also used for discrete time observations using the statements like Theorem 3 of Alodat and Olenko [2] or Lemma 1 of Leonenko and Taufer [45].…”

Section: Introductionmentioning

confidence: 99%

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Ivanov

Leonenko

Orlovskyi

2019

Stat Inference Stoch Process

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A continuous-time nonlinear regression model with LГқvy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper. IntroductionThe paper is focused on such an important aspect of the study of regression models with correlated observations as an estimation of random noise functional characteristics. When considering this problem the regression function unknown parameter becomes nuisance and complicates the analysis of noise. To neutralise its presence, we must estimate the parameter and then build estimators, say, of spectral density parameter of a stationary random noise using residuals, that is the difference between the values of the observed process and fitted regression function.So, in the first step we employ the least squares estimator (LSE) for unknown parameter of nonlinear regression, because of its relative simplicity. Asymptotic properties of the LSE in nonlinear regression model were studied by many authors. Numerous results on the subject can be found in monograph by Ivanov and Leonenko [34], Ivanov [32].

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Weak convergence of weighted additive functionals of long-range dependent fields

Cited by 9 publications

References 24 publications

On asymptotics of discretized functionals of long-range dependent functional data

On asymptotics of discretized functionals of long-range dependent functional data

Estimation of cyclic long‐memory parameters

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

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