Multinomial and empirical likelihood under convex constraints

Grendár, Marian, 1969-

Multinomial and empirical likelihood under convex constraints : directions of recession, Fenchel duality, the PP algorithm / Marian Grendár, Vladimír Špitalský. -- The primal problem of multinomial likelihood maximization restricted to a convex closed subset of the probability simplex is studied. A solution of this problem may assign a positive mass to an outcome with zero count. Such a solution cannot be obtained by the widely used, simplified Lagrange and Fenchel duals. Related flaws in the simplified dual problems, which arise because the recession directions are ignored, are identified and the correct Lagrange and Fenchel duals are developed.

In Electronic Journal of Statistics. -- [Shaker Heights] : Institute of Mathematical Statistics, 2017. -- ISSN 1935-7524. -- Vol. 11, no. 1 (2017), pp. 2547-2612