Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 267--284

EFFICIENCY OF BLOCK DESIGNS UNDER STATIONARY SECOND-ORDER AUTOREGRESSIVE ERRORS

By

MARTIN O. GRONDONA

And

NOEL CRESSIE, Iowa State University

 

SUMMARY. This article presents sufficient conditions for the universal optimality of block designs when observations within blocks follow a second order autoregressive (AR(2)) process. The optimal design is then compared to first-order nearest-neighbor (NN) balanced complete block designs, which are much easier to construct. In terms of A-optimality and D-optimality criteria, first-order NN balanced designs are shown to be very efficient. Further more, they are more efficient (in terms of average variance of treatment differences)than randomized complete block designs. Finally, the robustness of first-order NN balanced complete block designs, against a misspecified AR(1) error model, is assessed.

 

AMS (1980) subject classification. 62K10,62K0560G60

Key words and phrases. Autoregressive models, block design, efficiency, nearest-neighbor balance, universal optimality

FULL PAPER.

This article in Mathematical Reviews.