Invariant ordering and order preservation
D. R. Jensen · Lecture notes-monograph series · 1984
Suppose( J is a group of one-to-one transformations of a set Λ onto Λ, M is maximal invariant taking values in an ordered set (M,^M), and^is an ordering on Jr induced from ^ M .Properties of (Λ ,^) are studied in Part I including lattice properties and order preservation.Examples include an ordering on 7 nXm having properties of Loewner's (1934) ordering for Hermitian varieties, a unitary ordering on 7 nXm giving a lattice, and orderings on T? invariant under various groups.Applications to a variety of problems in statistics and applied probability are given in Part II.. PART I. THEORY