In this note we study the behavior of maximum quasilikelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Our main results are related to guarantees on existence, strong consistency and mean square...

We define the primal and dual linear programming problems involving interval numbers as the way of traditional linear programming problems. We discuss the solution concepts of primal and dual linear programming problems involving interval numbers without converting them to classical linear programming problems. By introducing new arithmetic operations between interval numbers, we prove the weak...

Finite-dimensional linear programs satisfy strong duality (SD) and have the “dual 8 pricing” (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of 9 the right-hand-side vector, there exists a dual solution that correctly “prices” the perturbation by 10 computing the exact change in the optimal objective function value. These properties may fail in 11 semi-inf...

In this paper we give very sharp bounds for the distance between regularity and strong regularity. The solution of this problem uses a general matrix analogue [18] of the Perron-Frobenius Theory. This theory has been graded as a challenge problem for future research by the International Linear Algebra Society [7]. An interval matrix [A] ∈ IIMn(IR) is called regular, if every A ∈ [A] is nonsingu...

Robust (M-) estimation in linear models generally involves statistical functional processes. For drawing statistical conclusions (in large samples), some (uniform) linear approximations are usually needed for such functionals. In this context, the role of Hadamard differentiability is critically examined in this dissertation. In particular, the concept of the second-order Hadamard differenti-ab...