Hypothesis testing of one sample mean vector in distributed frameworks

Abstract

Distributed frameworks are commonly used in the setting where data are stored in k different local machines and cannot be merged due to privacy protections or the huge sample size. For a random vector X ∈ R p with expectation μ , testing the mean vector H 0 : μ = μ 0 vs H 1 : μ ≠ μ 0 for a given vector μ 0 is a basic problem in statistics. In distributed frameworks, the computation of the centralized test statistics is not privacy-preserving and often requires heavy communication costs, which can be a burden when p or k is large. To deal with this problem, we extend two commonly used centralized test statistics to the distributed ones based on the divide and conquer technique. It is observed that the proposed test statistics are effective and can reduce communication costs and computation complexity. Numerical results confirm the theoretical findings.