Nearest neighbor balanced block designs for autoregressive errors

Mamadou Koné () and Annick Valibouze ()
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Mamadou Koné: Sorbonne Université
Annick Valibouze: Sorbonne Université

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 3, No 1, 312 pages

Abstract: Abstract In this paper we study the problem of finding neighbor optimal designs for a general correlation structure. We give universal optimality conditions for nearest-neighbor (NN) balanced block designs when observations on the same block are modeled by an autoregressive AR(m) process with arbitrary order m. The cases $$m=1,2$$ m = 1 , 2 have been studied by Grondona and Cressie (Sankhyā Indian J Stat Ser A 55(2):267–284, 1993) for AR(2) and by Gill and Shukla (Biometrika 72(3):539–544, 1985a, Commun Stat Theory Methods 14(9):2181–2197, 1985b) and Kunert (Biometrika 74(4):717–724, 1987) for AR(1); we extend these results to the cases $$m \ge 3$$ m ≥ 3 .

Keywords: Autoregressive model; Block design; Generalized least squares estimation; Nearest-neighbor balanced; Universally optimal (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-020-00770-6

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