Minimization of divergences on sets of signed measures
By Michel Broniatowski, Amor Keziou. 2010
103 citations recorded by the source corpus.
We consider the minimization problem of $\phi$-divergences between a given probability measure $P$ and subsets $\Omega$ of the vector space $\mathcal{M}_\mathcal{F}$ of all signed finite measures which integrate a given class $\mathcal{F}$ of bounded or unbounded measurable functions. The vector space $\mathcal{M}_\mathcal{F}$ is endowed with the weak topology induced by the class $\mathcal{F}\cup \mathcal{B}_b$ where $\mathcal{B}_b$ is the class of all bounded measurable functions. We treat the problems of existence and characterization of the $\phi$-projections of $P$ on $\Omega$. We consider also the dual equality and the dual attainment problems when $\Omega$ is defined by linear constraints.
Subfields: Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/b55e0353fc921d292664ae9dc87ebcfad9077935
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In Management Science and Operations Research
Citations in the corpus
- Divergences and Duality for Estimation and Test under Moment Condition Models (2010, methodology): “ hull of the data (X1,...,Xn). This is precisely what is checked in Owen (1990), p. 100, for the EL method; see also Owen (2001). Fortheasymptotic counterpartoftheaboveresults we have; see Theorem 1inBroniatowski and Keziou (2006): 14 MICHELBRONIATOWSKI 1ANDAMORKEZIOU ,2 Proposition 4.2. Let θbe a g”
- Decomposable Pseudodistances and Applications in Statistical Estimation (2011, methodology): “We consider the case of no outliers and the cases of 5% or 10% outliers coming from the model N (2, 1).”