The Annals of Statistics

On MSE-optimal crossover designs

Christoph Neumann and Joachim Kunert

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In crossover designs, each subject receives a series of treatments one after the other. Most papers on optimal crossover designs consider an estimate which is corrected for carryover effects. We look at the estimate for direct effects of treatment, which is not corrected for carryover effects. If there are carryover effects, this estimate will be biased. We try to find a design that minimizes the mean square error, that is, the sum of the squared bias and the variance. It turns out that the designs which are optimal for the corrected estimate are highly efficient for the uncorrected estimate.

Article information

Ann. Statist., Volume 46, Number 6A (2018), 2939-2959.

Received: December 2016
Revised: October 2017
First available in Project Euclid: 7 September 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs

Optimal design crossover design MSE-optimality


Neumann, Christoph; Kunert, Joachim. On MSE-optimal crossover designs. Ann. Statist. 46 (2018), no. 6A, 2939--2959. doi:10.1214/17-AOS1644.

Export citation


  • Azaï s, J.-M. and Druilhet, P. (1997). Optimality of neighbour balanced designs when neighbour effects are neglected. J. Statist. Plann. Inference 64 353–367.
  • Bose, M. and Dey, A. (2009). Optimal Crossover Designs. World Scientific, Hackensack, NJ.
  • Chêng, C. S. and Wu, C.-F. (1980). Balanced repeated measurements designs. Ann. Statist. 8 1272–1283.
  • David, O., Monod, H., Lorgeou, J. and Philippeau, G. (2001). Control of interplot interference in Grain Maize. Crop Science 41 406.
  • Horn, R. A. and Johnson, C. R. (2013). Matrix Analysis, 2nd ed. Cambridge Univ. Press, Cambridge.
  • Kiefer, J. (1975). Construction and optimality of generalized youden designs. In A Survey of Statistical Design and Linear Models (J. N. Srivastava, ed.) 333–366. North-Holland, Amsterdam.
  • Kunert, J. (1983). Optimal design and refinement of the linear model with applications to repeated measurements designs. Ann. Statist. 11 247–257.
  • Kunert, J. and Sailer, O. (2006). On nearly balanced designs for sensory trials. Food Qual. Prefer. 17 219–227.
  • Kushner, H. B. (1997). Optimal repeated measurements designs: The linear optimality equations. Ann. Statist. 25 2328–2344.
  • Kushner, H. B. (1998). Optimal and efficient repeated-measurements designs for uncorrelated observations. J. Amer. Statist. Assoc. 93 1176–1187.
  • MacFie, H. J. H., Bratchell, N., Grenhoff, K. and Vallis, L. V. (1989). Designs to balance the effect of order of presentation and first-order carry-over effects in hall tests. J. Sens. Stud. 4 129–148.
  • Ozan, M. O. and Stufken, J. (2010). Assessing the impact of carryover effects on the variances of estimators of treatment differences in crossover designs. Stat. Med. 29 2480–2485.
  • Senn, S. (2002). Cross-over Trials in Clinical Research, 2nd ed. Statistics in Practice. Wiley, Chichester.
  • Shah, K. R. and Sinha, B. K. (1989). Theory of Optimal Designs. Lecture Notes in Statistics 54. Springer, New York.