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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Thursday, August 3, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Olivier Thas}
\centerline{\sl Ghent Universit}
\centerline{\sl Belgium}
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\centerline{\bf A Nonparametric Test for Independence Based on Sample Space Partitions}
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The research that will be presented is actually part of a study of a more
general nonparametric test for goodness-of-fit (GOF). These GOF-methods for
continuous data can in general be divided into two groups: the more recent
techniques that often rely on smoothing methods, and some classical methods
that are based on e.g. Pearson's
$\chi^2$-test applied to the categorized continuous data. For the latter
class one has to decide how the data should be categorized, i.e. how the
sample space should be  partitioned. 

Another way around the problem is to consider a random sample of
rectangular sample space partitions (SSP); each partition implying a
contingency table of the categorized data. Then in each implied table e.g.
a Pearson $\chi^2$-test for independence is performed and all these test
statistics are combined into one test statistic. For a fixed SSP-size, the
asymptotic null distribution is proven, as well as its consistency for
essentially any alternative. In the simulation study that will be
presented, it is suggested that the small sample power depends on the
SSP-size used for a given alternative. Avoiding the SSP-size choice and
improving the overall power characteristics is achieved by constructing a
data-driven version of the test, i.e. the partition size is derived from
the data by means of e.g. a Schwartz criterion.

A simulation study is presented in which the proposed tests are compared to
other tests. 

To conclude some extensions are suggested. These include the generalization
to GOF-tests, and a graphical technique to visualize the type of dependence.

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