Seminar of the Department of Medical Statistics & Evaluation
IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE
The Hammersmith campus
8th July 1998, 3.00 - 5.30 pm, (tea, 4.00pm)
"Bootstrap Location Tests:
Theoretical and Practical Aspects in the One-Sample Case"
Dr Karin Wolf-Ostermann (3.00pm)
University of Siegen, Germany
and
"Allelic association in complex diseases: the TDT and extensions"
Dr John Whittaker (4.30pm)
University of Reading
Venue:
Talk - Seminar room No. (tba), Sub-Basement of Commonwealth Building
Imperial College School of Medicine, entrance via ground floor and
elevator
The Hammersmith campus, Du Cane Road, London W12 ONN
Tea - Seminar room of the Department of Medical Statistics & Evaluation
Basement of Commonwealth Building
Phone 0181 383 3255, Fax 0181 383 8573
Nearest Underground (Central line):
East Acton (10 min walk), White City (15 min walk)
Buses: Stop at Hammersmith Hospital
No. 7 from Russell Square via Paddington to East-Acton
No. 70 from South Kensington via Notting Hill Gate to Acton
No. 72 from Roehampton via Hammersmith and Shepherd's Bush
to East-Acton
No. 283 from Barnes via Hammersmith and Shepherd's Bush to
East-Acton
location
http://www.streetmap.co.uk/streetmap.dll?grid2map?X=522600&Y=181000&arrow=Y&
zoom=5
http://www.publications.ad.ic.ac.uk/maps/images/pdfs/wldn_locations.pdf
(Imperial College)
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Abstracts:
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talk 3.00pm:
"Bootstrap Location Tests Theoretical and Practical Aspects in the
One-Sample Case"
Karin WOLF-OSTERMANN (University of Siegen)
Although resampling techniques like the bootstrap have been known for
many years, most of the work on bootstrap methods concerns asymptotic
results.
Asymptotic properties deal with potentially large samples, but we also need
empirical investigations of bootstrap properties for finite samples. Since
bootstrap methods are based on generating virtual samples from a given data
set
an underlying sample itself can influence the outcome of bootstrap
procedures seriously.
In a series of papers Beran (1984, 1986,1988) proposed bootstrap techniques
for
hypothesis testing and proved the uniform consistency of simulated power
functions.
We use his test statistic approach to estimate critical values and power
functions.
Following the demands of Young (1994) we show that the breakdown of the
bootstrap-t-test
can be characterized empirically (Wolf-Ostermann (1996)). Based on these
investigations
we develop different adaptive bootstrap tests for a location parameter which
depend on
empirical measures of the underlying sample (Wolf-Ostermann (1997,1998)).
The combination
of bootstrap and adaptive methods for constructing test procedures in this
way is a new
approach which is not wide-spread in current statistical literature.
Since theoretical results can only be achieved asymptotically, we show that
all proposed
bootstrap tests have asymptotic level alpha and the estimated power
functions are uniformly
or pointwise consistent. For the finite sample case the performance of the
proposed test
procedures is analysed by a simulation study. The research concentrates on
the case of
small and moderate sample sizes which are of interest for the practical use
of bootstrap
tests. Comparisons of the corresponding tests are carried out by considering
observed
significance levels and power.
Keywords: adaptive test, asymptotic power, bootstrap, simulated power
References
Beran, R. (1984): Bootstrap methods in statistics.
Jber. der Dt. Math. Verein., 86, 14-30.
Beran, R. (1986): Simulated power functions.
Ann. Statist., 14, 151-173.
Beran, R. (1988): Prepivoting test statistics: A bootstrap view
of asymptotic refinements.
J. Amer. Statist. Assoc., 83, 687-697.
Wolf-Ostermann, K. (1996): The Influence of Skewness and Kurtosis
on the Performance of Bootstrap Location Tests
for Moderate Sample Sizes.
in: Prat, A. & Ripoll, E. (eds)
COMPSTAT96 - Short Communications, 143-144.
Wolf-Ostermann, K. (1997): Bootstrap-Testverfahren für
Lokationsparameter univariater Verteilungen.
Ph.D. Thesis, Dept. of Statistics,
University of Dortmund.
Wolf-Ostermann, K. (1998): An Approach for Adaptive Bootstrap Testing
based on Power Functions.
in: Payne, R. & Lane, P. (eds)
COMPSTAT98 - Short Communications, 125-126.
Young, G.A. (1994): Bootstrap: More than a stab in the dark?
Statist. Science, 9, 382-415.
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talk 4.30pm:
"Allelic association in complex diseases: the TDT and extensions"
John WHITTAKER (University of Reading)
There has been much recent interest in the possibility of using
allelic association to locate the genes contributing to complex
human diseases. Data is often assumed to consist of genotypic
information on family units comprising an affected individual and
both parents of that individual. We review briefly the key
concepts involved in the analysis of such data, and point out some
connections between the many methods of analysis that have been
suggested. Some extensions to the standard methods are suggested
to allow the simultaneous analysis of several disease loci and to
raise the possibility of obtaining more precise inferences on
disease gene location by an alternative parameterisation of the
standard model. This seems to be best done in a Bayesian
framework: the advantages and disadvantages of the Bayesian
approach will be discussed briefly.
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