Existence and uniqueness of risk-sensitive estimates

25. James T. Lo, Thomas Wanner:
    Existence and uniqueness of risk-sensitive estimates
    IEEE Transactions on Automatic Control 47(11), pp. 1945-1948, 2002.

Abstract

Risk-sensitive criteria have been used to derive robust filters, identifiers and controllers. The fundamental issues of existence and uniqueness of an estimate of a random variable given a random vector with respect to an order-$(\lambda, p)$ risk-sensitive criterion are studied in this paper. More precisely, we prove the existence of a unique risk-sensitive estimate provided $\lambda > 0$ and $p > 1$. For the remaining cases, a general existence result is not available at this time. We do however prove the existence in certain special cases. Moreover, we present examples with uncountably many optimal risk-sensitive estimates, i.e., exhibiting an extremely high level of nonuniqueness.

Links

The published version of the paper can be found at https://doi.org/10.1109/TAC.2002.804458.

Bibtex

@article{lo:wanner:02a,
   author = {James T. Lo and Thomas Wanner},
   title = {Existence and uniqueness of risk-sensitive estimates},
   journal = {IEEE Transactions on Automatic Control},
   year = 2002,
   volume = 47,
   number = 11,
   pages = {1945--1948},
   doi = {10.1109/TAC.2002.804458}
   }