Parameter estimation in linear regression driven by a Gaussian sheet

Baran, Sándor; Sikolya, Kinga

doi:10.1007/bf03651393

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…To illustrate the differences between K-and D-optimal designs, computer simulations using Matlab R2014a are performed. In general, the driving stationary Ornstein-Uhlenbeck processes and fields of models (2.1) and (3.1), respectively, can be simulated either with the help of discretization (see, e.g., Gillespie, 1996) or using their Karhunen-Loève expansions based on representations (2.3) and (3.3) (Jaimez and Bonnet, 1987;Baran and Sikolya, 2012). However, in our simulation study, due to the small number of locations, it is sufficient to draw samples from the corresponding finite dimensional distributions.…”

Section: Simulation Resultsmentioning

confidence: 99%

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K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

Baran

2017

Journal of Statistical Planning and Inference

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Continuous random processes and fields are regularly applied to model temporal or spatial phenomena in many different fields of science, and model fitting is usually done with the help of data obtained by observing the given process at various time points or spatial locations. In these practical applications sampling designs which are optimal in some sense are of great importance. We investigate the properties of the recently introduced K-optimal design for temporal and spatial linear regression models driven by Ornstein-Uhlenbeck processes and sheets, respectively, and highlight the differences compared with the classical D-optimal sampling. A simulation study displays the superiority of the K-optimal design for large parameter values of the driving random process.

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Section: Simulation Resultsmentioning

confidence: 99%

“…where W(s, t), s, t ∈ R, is a standard Brownian sheet (Baran et al, 2003;Baran and Sikolya, 2012). Again, we assume that the parameters β, γ and σ of the OU sheet U (s, t) driving model (3.1) are known.…”

Section: Comparison Of Equidistant Designsmentioning

confidence: 99%

K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

Baran

2017

Journal of Statistical Planning and Inference

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“…where W(s, t), s, t ∈ R, is a standard Brownian sheet (Baran et al, 2003;Baran and Sikolya, 2012). Covariance structure (2.2) implies that for…”

Section: Statistical Modelmentioning

confidence: 99%

Optimal designs for parameters of shifted Ornstein–Uhlenbeck sheets measured on monotonic sets

Baran¹,

Stehlík²

2015

Statistics & Probability Letters

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Measurement on sets with a specific geometric shape can be of interest for many important applications (e.g. measurement along the isotherms in structural engineering). In the present paper the properties of optimal designs for estimating the parameters of shifted OrnsteinUhlenbeck sheets, that is Gaussian two-variable random fields with exponential correlation structures, are investigated when the processes are observed on monotonic sets. Substantial differences are demonstrated between the cases when one is interested only in trend parameters and when the whole parameter set is of interest. The theoretical results are illustrated by computer experiments and simulated examples from the field of structure engineering. From the design point of view the most interesting finding of the paper is the loss of efficiency of the regular grid design compared to the optimal monotonic design.

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“…where W(s, t), s, t ∈ R, is a standard Brownian sheet (Baran et al, 2003;Baran and Sikolya, 2012). As can be visible from relation (1.2) between rates and parameters A, µ and B of the modified Arrhenius model, the second variable s is missing from trend since it is not chemically understood as driving mechanism of chemical kinetics, however, in this context it is an environment variable.…”

Section: Introductionmentioning

confidence: 99%

Optimal designs for the methane flux in troposphere

Baran

Sikolya

Stehlík

2015

Chemometrics and Intelligent Laboratory Systems

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The understanding of methane emission and methane absorption plays a central role both in the atmosphere and on the surface of the Earth. Several important ecological processes, e.g., ebullition of methane and its natural microergodicity request better designs for observations in order to decrease variability in parameter estimation. Thus, a crucial fact, before the measurements are taken, is to give an optimal design of the sites where observations should be collected in order to stabilize the variability of estimators. In this paper we introduce a realistic parametric model of covariance and provide theoretical and numerical results on optimal designs. For parameter estimation D-optimality, while for prediction integrated mean square error and entropy criteria are used. We illustrate applicability of obtained benchmark designs for increasing/measuring the efficiency of the engineering designs for estimation of methane rate in various temperature ranges and under different correlation parameters. We show that in most situations these benchmark designs have higher efficiency.Comment: 25 pages, 4 figure

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Parameter estimation in linear regression driven by a Gaussian sheet

Cited by 4 publications

References 14 publications

K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

K-optimal designs for parameters of shifted Ornstein–Uhlenbeck processes and sheets

Optimal designs for parameters of shifted Ornstein–Uhlenbeck sheets measured on monotonic sets

Optimal designs for the methane flux in troposphere

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