A note on step-up test in orthogonal saturated designs

作者：Wu Samuel S^*; Wang Weizhen

来源：Journal of Statistical Planning and Inference, 2008, 138(10): 3149-3156.

DOI：10.1016/j.jspi.2007.12.006

• stochastic ordering
• effect sparsity
• experimentwise error rate
• non-central chi-squared distribution

Let X-i be the ith order statistic of (beta) over cap (2)(j) for 1 <= j <= k, where (beta) over cap (j)'s follow independent normal distributions with respective means beta(j) and common variance sigma(2). In this paper, we provide a stochastic ordering of the random vector T = (X-2/X-1, 2X(3)/(X-1 + X-2), ..., (m-1)X-m/Sigma(m-1)(j=1) X-j) as the beta(j)'s change for any given 2 <= m <= k. With this result and the assumption of effect sparsity, we construct a step-up simultaneous testing procedure that strongly controls experimentwise error rate for a sequence of null hypotheses regarding the number of negligible effects (zero beta(j)'s) in orthogonal saturated designs.

• 出版日期2008-10-1
• 单位天津大学