Optimal and efficient designs for fMRI experiments via two-level circulant almost orthogonal arrays

Xiao Nan Lu, Miwako Mishima, Nobuko Miyamoto, Masakazu Jimbo

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate a class of optimal circulant {0,1}-arrays other than the previously known class of optimal designs for fMRI experiments with a single type of stimulus. We suppose throughout the paper that n≡2(mod4) and discuss the asymptotic optimality and the D-efficiency of k×n circulant almost orthogonal arrays (CAOAs) with 2 levels (presence/absence of the stimulus), strength 2 and bandwidth 1, denoted by CAOA(n,k,2,2,1). We show that for n≡2(mod4) the largest possible value of k for statistically optimal CAOA(n,k,2,2,1) cannot exceed n∕2. We also clarify that CAOA(n,k,2,2,1) with high D-efficiency and k greater than n∕2 can be obtained via perfect binary sequences. By applying algebraic constructions for perfect binary sequences and by computer search, lists of such efficient CAOAs and the new class of optimal CAOAs are provided.

Original languageEnglish
Pages (from-to)33-49
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume213
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Circulant almost orthogonal array
  • Design efficiency
  • Hemodynamic response function

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