Asymptotic properties of parameter estimates for random fields with tapered data

Alomari, Huda Mohammed; Frías, María Pilar; Leonenko, Nikolai; Ruiz-Medina, M. D.; Sakhno, Lyudmyla; Torres, Anna

doi:10.1214/17-ejs1315

Cited by 11 publications

(19 citation statements)

References 41 publications

(71 reference statements)

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“…We consider the Gegenbauer random process

X false(t false), t \in double-struckZ

; see Alomari et al (), Espejo et al (), and the references therein. This random process satisfies the following equation:

Δ_{u}^{d} X (t) : = {(1 - 2 u B + B^{2})}^{d} X (t) = ε_{t},

where

{normalΔ}_{u}^{d}

is the fractional difference operator given by

Δ_{u}^{d} = {(1 - 2 u B + B^{2})}^{d} = {(1 - 2 \cos (ν) B + B^{2})}^{d} = {[(1 - e^{i ν} B) (1 - e^{- i ν} B)]}^{d};

B denotes the backward‐shift operator for the time coordinate t , that is, BX t = X t −1 ,

u = \cos ν

(i.e.,

ν = \arccos false(u false), false| u false| \leq 1 false),

d \in false(- \frac{1}{2}, \frac{1}{2} false)

; and ε t is a zero‐mean white noise with the common variance

E false(ε_{t}^{2} false) = σ_{ε}^{2} .

…”

Section: Simulation Studiesmentioning

confidence: 99%

“…We consider the Gegenbauer random process X(t), t ∈ ℤ; see Alomari et al (2017), Espejo et al (2015), and the references therein. This random process satisfies the following equation:…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Consistency and asymptotic normality of MCEs for parameters of Gegenbauer random processes and fields were obtained in Espejo, Leonenko, Olenko, and Ruiz-Medina (2015). More details on the current state of the MCE theory for long-memory processes and additional references can be found in Alomari et al (2017).…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, the results in Alomari et al (), Espejo et al (), and Leonenko and Sakhno () for Gegenbauer‐type long‐memory models use specific weight functions that approach zero at the known singularity point, which, for example, was estimated before or determined by particular applications. It is not obvious how to modify these methods if locations of singularities are unknown.…”

Section: Introductionmentioning

confidence: 99%

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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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“…We consider the Gegenbauer random process

X false(t false), t \in double-struckZ

; see Alomari et al (), Espejo et al (), and the references therein. This random process satisfies the following equation:

Δ_{u}^{d} X (t) : = {(1 - 2 u B + B^{2})}^{d} X (t) = ε_{t},

where

{normalΔ}_{u}^{d}

is the fractional difference operator given by

Δ_{u}^{d} = {(1 - 2 u B + B^{2})}^{d} = {(1 - 2 \cos (ν) B + B^{2})}^{d} = {[(1 - e^{i ν} B) (1 - e^{- i ν} B)]}^{d};

B denotes the backward‐shift operator for the time coordinate t , that is, BX t = X t −1 ,

u = \cos ν

(i.e.,

ν = \arccos false(u false), false| u false| \leq 1 false),

d \in false(- \frac{1}{2}, \frac{1}{2} false)

; and ε t is a zero‐mean white noise with the common variance

E false(ε_{t}^{2} false) = σ_{ε}^{2} .

…”

Section: Simulation Studiesmentioning

confidence: 99%

“…We consider the Gegenbauer random process X(t), t ∈ ℤ; see Alomari et al (2017), Espejo et al (2015), and the references therein. This random process satisfies the following equation:…”

Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of cyclic long‐memory parameters

Alomari

Ayache

Fradon

et al. 2019

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the one hand, we find work on the modeling of long memory dependent multivariate random fields estimation procedures. Among these studies, we have the paper of Alomari and al. (2017) entitled "Ibragimov minimum contrast estimators based on tapered data of Gaussian stationary random fields".…”

Section: Introductionmentioning

confidence: 99%

Parametric Estimation of Long Memory Multivariate Gaussian random fields

N'dri¹,

Kamagaté²,

Hili³

2021

jas

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A spatial functional count model for heterogeneity analysis in time

Torres-Signes

Frías

Mateu

et al. 2021

Stoch Environ Res Risk Assess

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A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive 2 -valued processes (SAR 2 processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality.

show abstract

Asymptotic properties of parameter estimates for random fields with tapered data

Abstract: In this paper we present novel results on the asymptotic behavior of the so-called Ibragimov minimum contrast estimates. The case of tapered data for various models of Gaussian random fields is investigated.MSC 2010 subject classifications: Primary 62F12, 62M30; secondary 60G60.

Cited by 11 publications

References 41 publications

Estimation of cyclic long‐memory parameters

Estimation of cyclic long‐memory parameters

Parametric Estimation of Long Memory Multivariate Gaussian random fields

A spatial functional count model for heterogeneity analysis in time

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