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Date: Friday 28 October 2011 at 3pm
Location: 6301 JCMB
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Joachim Kunert (Dortmund University)
Optimal block designs for treatment control comparisons with correlated
errors
Abstract
There is an extensive literature on optimal and efficient designs for
comparing /t/ test (or new) treatments with a control (or standard
treatment) - see Majumdar (1996). However, almost all results assume the
observations are uncorrelated. In many situations, it is more realistic
to assume that observations in the same block are positively correlated,
and there has been much interest in this case when all contrasts are of
equal interest - see, for example, Martin (1996).Assuming that the
estimation uses ordinary least-squares, Bhaumik (1990) found optimal
within-block orderings under a first-order nearest-neighbour model NN(1)
among some designs that would have been optimal test-control designs
under independence. Cutler (1993) obtained some optimality results under
a first-order autoregressive process AR(1) on the circle or the line,
assuming generalised least-squares estimation for a known dependence.
There are also some brief examples and discussion of the correlated case
in Martin & Eccleston (1993, 2001). Here, we concentrate on generalised
least-squares estimation for a known covariance. Results for
independence, and Cutler's (1993) results for the AR(1), are for
specific combinations of /t/, /b/, /k/, and use integer minimisation to
ensure an optimal design exists. Here, we assume that the number of
blocks /b/ is large enough for an optimal design to exist, and consider
the form of that optimal design. This method may lead to exact optimal
designs for some /b/, /t/, /k/, but usually will only indicate the
structure of an efficient design for any particular /b/, /t/, /k/, and
yield an efficiency bound, usually unattainable. The bound and the
structure can then be used to investigate efficient finite designs.
Tea and coffee will be available after the seminar in the Mathematics
Common Room (5212).
The webpage for the seminar:
http://www.maths.ed.ac.uk/~nbochkin/StatisticsSeminar.html
This seminar is a part of the Maxwell Institute seminar series.
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Dr Natalia Bochkina
Lecturer in Statistics
School of Mathematics
King’s Buildings
University of Edinburgh
Mayfield Road
Edinburgh, EH9 3JZ
Tel: 0131 650 8597
Email: [log in to unmask]
Webpage: http://www.maths.ed.ac.uk/~nbochkin/
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