On Nested Orthogonal Arrays

Orthogonal arrays belong to an important and high-profile area of combinatorics and statistics. Nested orthogonal arrays were introduced to construct nested space-filling designs which have been proposed for conducting multiple computer experiments with different levels of accuracy where the expensive one of higher accuracy to be nested in a larger and relatively inexpensive one of lower accuracy. Nested orthogonal arrays are closely related to incomplete orthogonal arrays which are essential in combinatorial design theory and extensively used as ingredients in the construction of other types of designs. In this thesis, we studied the construction and existence of nested orthogonal arrays by employing the corresponding techniques in combinatorial design theory.By modifying some known combinatorial constructions of orthogonal array or in-complete orthogonal array, we established several combinatorial constructions of nested orthogonal array:t-balanced design construction, Wilson-type construction, Identifi-cation construction, Concatenation construction and Difference matrix construction.As an application of the established constructions, the following main results about the existence of nested orthogonal array are obtained:(1) The existence spectrum of NOA((st,rt),t+1,(s,r),t) is completely determined;(2) The existence spectrum of LNOA((4r2,r2),4,(2r, r),2) is almost completely determined;(3) The existence spec-trum of NOA((2s2,r2),4,(s,r),2) is completely determined;(4) Part of the existence result of NOA((3s2,2r2),4,(s,r),2) is obtained, furthermore the corresponding exis-tence result of NOA((λs2,μr2),4,(s,r),2) is obtained;(5) Two infinite class of nested orthogonal array with strength3and degree6are obtained.