Bounds on normal approximation of Latin hypercube and ortrogonal array samplings

Abstract

This thesis consists of three parts. In the first part, a constant on a uniform bound on normal approximation for latin hypercube sampling is obtained assuming the finiteness of absolute third moment. Under the same condition, we derive a constant on a uniform bound on a combinatorial central limit theorem in the second part. The last part contains a proof of a non-uniform bound on normal approximation of randomized orthogonal array sampling designs under the finiteness of sixth moment.