While many of you may not be able to get to this seminar, some
may be interested in the abstract and references.
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SEMINAR, London, 8th Oct 98, 4.00 pm - Imperial College, Hammersmith Campus

Berthold Lausen ([log in to unmask])

Centre for Epidemiology and Biostatistics Seminars (CEBS)

IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE
The Hammersmith campus

8th October 1998, 4.00pm, (tea, 3.30pm)

Title: "Bootstrap Location Tests: Theoretical and
Practical Aspects in the One-Sample Case"

Speaker: Dr Karin Wolf-Ostermann
(University of Siegen, D-57068 Siegen, Germany)

Venue:
Tea - Seminar room of the Department of Medical Statistics
& Evaluation, Basement of Commonwealth Building,
entrance via ground floor and elevator
Talk - Seminar room, Sub-Basement of Commonwealth Building
entrance via ground floor and elevator
Imperial College School of Medicine
The Hammersmith campus, Du Cane Road, London W12 ONN
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

Abstract:
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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-- 
Dr.Simon Peters, [log in to unmask],Tel:+44(0)161-275-4830,FAX(275-4928)
School of Economic Studies, University of Manchester, UK


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