On sequential estimation of the mean of a multidimensional gaussian process

Ibabbola, Pilab; Vélez, Ricardo

doi:10.1080/02331889008802257

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…Let H i be the completion of H;+with all 7-null sets in F. Sufficiency and transitivity of {HZ},,Ri (the arguments for proving this fact are similar to those ones in (Ibarrola and VClez (1990)) together with convexity of the loss function lead us to the conclusion that we can restrict ourselves to considering deterministic invariant sequential rules such that d,(Tcq<) = d,([) + g and r(T,<) = T(<) for all < E E, g E Rk, z E R:,i > 0, where r is a stopping point with respect to {Hl,),ERt.…”

Section: Invariant Sequential Estimation Of the Parametermentioning

confidence: 89%

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

Ibarrola

Różański

Vélez³

1998

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In the paper we consider the problem of estimation for a multivariate Gaussian random field whose vector mean depends linearly of a multidimensional parameter 8. A Bayesian estimator is derived and its distributions are analyzed under the assumption that the covariance function is completely known. Further, an invariant structure is introduced and the optimal invariant terminal decision function obtained. Finally, assuming that the covariance function is known up to a parameter g ' we estimate the parameters 0 and a2 and prove some of their properties. The results of VBlez (1990), (1992), for multidimerisional stochastic processes are extended to the the present context and similar results are obtained.

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Section: Invariant Sequential Estimation Of the Parametermentioning

confidence: 89%

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

Ibarrola

Różański

Vélez³

1998

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“…According to (9), η/ (σ 2 1 + σ 2 2 ) has a χ 2 k distribution and is independent of U t , therefore the distribution…”

Section: Confidence Set For Identical Processesmentioning

confidence: 98%

“…In a previous paper [9] we obtained the estimator θ t defined by (1) in the case of a Wiener process with mean A(t)θ and covariance function K(t, t ) = K · (t ∧ t ).…”

Section: An Examplementioning

confidence: 99%

On Behrens–Fisher problem for continuous time Gaussian processes

Ibarrola

Vélez

2004

Linear Algebra and its Applications

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Our setting is the sequential observation of two continuous time multidimensional Gaussian processes whose mean vectors depend linearly on two multidimensional parameters and with different conditions about their covariance structures that will always include nuisance parameters. We analyze the Behrens-Fisher problem of comparing both parameters by means of a confidence set for their difference, with given confidence level and diameter. The random time needed to achieve this goal is also inspected.

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Inference in Multidimensional Gaussian Processes

Ibarrola¹,

Vélez²

1994

Decision Theory and Decision Analysis: Trends and Challenges

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On sequential estimation of the mean of a multidimensional gaussian process

Cited by 6 publications

References 3 publications

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

On Behrens–Fisher problem for continuous time Gaussian processes

Inference in Multidimensional Gaussian Processes

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