Mean estimation of Brownian sheet

Arató, Miklós

doi:10.1016/s0898-1221(97)00050-3

Cited by 7 publications

(10 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A Brownian sheet is a natural extension of the Brownian motion to a two-dimensional random field and is one of the most important examples of the Gaussian random fields. Furthermore, some properties has been studied such as a method to study Brownian sheet by the linear stochastic partial differential equations [1]. Many data sets have anisotropic nature in the sense that they have different geometric and probabilistic characteristics along different directions, hence fractional Brownian motion is not adequate for modeling such phenomena.…”

Section: Theoretical Structurementioning

confidence: 99%

Multi-scale Invariant Fields: Estimation and Prediction

Ghasemi¹,

Rezakhah²,

Modarresi³

2017

Preprint

View full text Add to dashboard Cite

Extending the concept of multi-selfsimilar random field we study multi-scale invariant (MSI) fields which have component-wise discrete scale invariant property. Assuming scale parameters as λ i > 1, i = 1, . . . , d and the parameter space as (1, ∞) d , the first scale rectangle is referred to the rectangle (1, λ 1 ) × . . . × (1, λ d ). Applying certain component-wise geometric sampling of MSI field, the harmonic-like representation and spectral density of the sampled MSI field are characterized. Furthermore, the covariance function and spectral density of the sampled Markov MSI field are presented by the variances and covariances of samples inside first scale rectangle. As an example of MSI field, a two-dimensional simple fractional Brownian sheet (sfBs) is demonstrated. Also real data of the precipitation in some area of Brisbane in Australia for two days (25 and 26 January 2013) are examined. We show that precipitation on this area has MSI property and estimate it as a simple MSI field with stationary increments inside scale intervals. This structure enables us to predict the precipitation in surface and time. We apply the mean absolute percentage error as a measure for the accuracy of the predictions.

show abstract

Section: Theoretical Structurementioning

confidence: 99%

Multi-scale Invariant Fields: Estimation and Prediction

Ghasemi¹,

Rezakhah²,

Modarresi³

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, if g ≡ 1 one can show that A and ζ gives back the corresponding quantities of [11,Theorem 2] and [12, Theorem 1.1].…”

Section: Remarkmentioning

confidence: 99%

“…In several cases the exact form of this random variable can be derived by a method proposed by Rozanov [10] based on linear stochastic partial differential equations. Arató [11] used Rozanov's method to find the MLE of the shift parameter of a shifted Wiener sheet observed on a special domain. In [12] the authors considered the model of Arató [11], and applying an essentially simpler direct discrete approach they found the MLE of the shift parameter under much weaker conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Arató [11] used Rozanov's method to find the MLE of the shift parameter of a shifted Wiener sheet observed on a special domain. In [12] the authors considered the model of Arató [11], and applying an essentially simpler direct discrete approach they found the MLE of the shift parameter under much weaker conditions. In the present paper the discrete approach is applied for a more general model and more complicated domain of observations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation of a shifted Wiener sheet

2010

View full text Add to dashboard Cite

show abstract

“…By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató, N. M. [3], an explicit formula is derived for the maximum likelihood estimator (MLE) of the shift parameter. The MLE is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process and its normal derivative along the curve Γ.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Mean of a Wiener Sheet

Baran

Pap

Zuijlen

2004

Statistical Inference for Stochastic Processes

View full text Add to dashboard Cite

A standard Wiener sheet shifted by an unknown parameter is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató, N. M. [3], an explicit formula is derived for the maximum likelihood estimator (MLE) of the shift parameter. The MLE is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process and its normal derivative along the curve Γ.Keywords. Wiener sheet, Radon-Nikodym derivatives, maximum likelihood estimator, stochastic integral along a curve, weighted integral of the normal derivative of a random process along a curve.

show abstract

Mean estimation of Brownian sheet

Cited by 7 publications

References 5 publications

Multi-scale Invariant Fields: Estimation and Prediction

Multi-scale Invariant Fields: Estimation and Prediction

Parameter estimation of a shifted Wiener sheet

Estimation of the Mean of a Wiener Sheet

Contact Info

Product

Resources

About