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= Parameter Estimation with Expected and Residual-at-Risk Criteria

- *Download:* [Pubs/ResatRisk_SCL.pdf .pdf]

- *Authors:* G. Calafiore, U. Topcu, L. El Ghaoui.

- *Status:* /Systems and Control Letters/, 58 (1), p.39-46, Jan 2009.

- *Abstract:*
In this paper we study a class of uncertain linear estimation problems
in which the data are affected by random uncertainty. We consider two estimation criteria, one based on minimization of the expected $\ell_1$ or $\ell_2$ norm residual and one based on minimization of the level within which the $\ell_1$ or $\ell_2$  norm residual is guaranteed to lie
with an a-priori fixed probability (residual at risk). The random uncertainty affecting the data is characterized by means of its first two statistical moments, and the above criteria are intended in a worst-case probabilistic sense, that is worst-case expectations and probabilities over all possible distribution having the specified moments are considered.
The ensuing estimation problems can be solved efficiently via convex programming, yielding exact solutions in the $\ell_2$ norm case and upper-bounds on the optimal solutions in the $\ell_1$ case.

#- *Related entries:*

- *Bibtex reference:*
~~~
{}{}
@article{CET:09,
	Author = {G. Calafiore and L. {El Ghaoui} and U. Topcu},
	Journal = {Systems and Control Letters},
	Title = {Parameter Estimation with Expected and Residual-at-Risk Criteria},
	Volume = {58},
	Number = {1},
	Pages = {39--46},
	Year = {2009}}
~~~