A lower bound for the pitman efficiency of Friedman type tests

An expression for the sharp lower bound for the efficiency of any Friedman type test with respect to the Friedman type test with optimal scores under weak model restrictions is given and calculated explicitely for the classical Friedman test.     

A note on the MIR closure and basic relaxations of polyhedra

Anderson et al. (2005) [1] show that for a polyhedral mixed integer set defined by a constraint system Ax≥b, along with integrality restrictions on some of the variables, any split cut is in fact a split cut for a basic relaxation, i.e., one defined by a subset of linearly independent constraints. This result implies that any split cut can be obtained as an intersection cut. Equivalence between split cuts obtained from simple disjunctions of the form x_j≤0 or x_j≥1 and intersection cuts was shown earlier for 0/1-mixed integer sets by Balas and Perregaard (2002) [4]. We give a short proof of the result of Anderson, Cornuéjols and Li using the equivalence between mixed integer rounding (MIR) cuts and split cuts.     

Concentration inequalities for nonlinear matroid intersection

In this work we propose new randomized rounding algorithms for matroid intersection and matroid base polytopes. We prove concentration inequalities for polynomial objective functions and constraints that has numerous applications and can be used in approximation algorithms for Minimum Quadratic Spanning Tree, Unrelated Parallel Machines Scheduling and scheduling with time windows and nonlinear objectives. We also show applications related to Constraint Satisfaction and dense polynomial optimization. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 541–571, 2015