On the theory of elliptically contoured distributions

Cambanis, Stamatis; Huang, Steel T.; Simons, Gordon

doi:10.1016/0047-259x(81)90082-8

Cited by 607 publications

(376 citation statements)

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“…1] to show that the joint random vector (ξ, η), as the image of ξ under the linear transformation I (N ξ ) , G ⊤ ⊤ , also follows an elliptically contoured distribution. This result allows us to invoke [11,Cor. 5] which guarantees that the conditional expectation of ξ given η is almost surely linear in η.…”

Section: Controller Information Structurementioning

confidence: 99%

An efficient method to estimate the suboptimality of affine controllers

Hadjiyiannis¹,

Goulart²,

Kuhn³

2010

UKACC International Conference on CONTROL 2010

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Abstract. We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy.

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Section: Controller Information Structurementioning

confidence: 99%

An efficient method to estimate the suboptimality of affine controllers

Hadjiyiannis¹,

Goulart²,

Kuhn³

2010

UKACC International Conference on CONTROL 2010

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“…The discussion in Section 1.1 implies the following statement (which is actually well known, see e.g. Lemma 3 in [CHS81]). Let ξ 1 and ξ 2 be independent Gamma distributed random variables with shape parameter k and l, respectively and with the same scale parameter.…”

Section: Local Equilibriummentioning

confidence: 84%

Local Equilibrium in Inhomogeneous Stochastic Models of Heat Transport

Nándori

2016

J Stat Phys

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Abstract. We extend the duality of Kipnis Marchioro and Presutti [KMP82] to inhomogeneous lattice gas systems where either the components have different degrees of freedom or the rate of interaction depends on the spatial location. Then the dual process is applied to prove local equilibrium in the hydrodynamic limit for some inhomogeneous high dimensional systems and in the nonequilibrium steady state for one dimensional systems with arbitrary inhomogeneity.

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“…In decreasing order of generality, we mention v-spherical distributions, as introduced in an, as yet, unpublished paper by the present authors (Cent.ER Discussion Paper 9374, Tilburg University), henceforth denoted by FOS, ly-spherical ciistributions, cíefined in Osiewalski and Steel (1993b), and spherical distributiou,, ati discussc~d in Ke~lker (1970), Cambanis et aL (1981), Dickey and Chen (1985) and Faufi ct a.l. (1990, Chapters 2-4).…”

Section: Introductionmentioning

confidence: 99%

The Continuous Multivariate Location-Scale Model Revisited: A Tale of Robustness

1994

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SummaryWe considcr the location-scale faniily of all nrultivariate continuous sampling distributions. Any tnodel from t.he subclass induced by fixing a particular distribution on the unit. sphc~re,, combine~d with a standard improper prior on the scale paranteter, will lead to the satne inícrcure ou location ancí observ~ables. This finding sheds light on many robustness rosults in lcss general rnodels and its implications are illustrated in a number of examples.

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On the theory of elliptically contoured distributions

Cited by 607 publications

References 1 publication

An efficient method to estimate the suboptimality of affine controllers

An efficient method to estimate the suboptimality of affine controllers

Local Equilibrium in Inhomogeneous Stochastic Models of Heat Transport

The Continuous Multivariate Location-Scale Model Revisited: A Tale of Robustness

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