EAN: 9783030125639

SPRINGERBRIEFS IN COMPUTER SCIENCE ASYMPTOTIC...

Stationarity is a very general  qualitative assumption  that can be assessed on the basis of
application specifics. It is thus a rather attractive assumption to base statistical analysis
on  especially for problems for which less general qualitative assumptions  such as
independence or finite memory  clearly fail. However  it has long been considered too general
to be able to make statistical inference. One of the reasons for this is that rates of
convergence  even of frequencies to the mean  are not available under this assumption alone.
Recently  it has been shown that  while some natural and simple problems  such as homogeneity 
are indeed provably impossible to solve if one only assumes that the data is stationary (or
stationary ergodic)  many others can be solved with rather simple and intuitive algorithms. The
latter include clustering and change point estimation among others. In this volume these
results are summarize. The emphasis is on asymptotic consistency  since this the strongest
property one can obtain assuming stationarity alone. While for most of the problem for which a
solution is found this solution is algorithmically realizable  the main objective in this area
of research  the objective which is only partially attained  is to understand what is possible
and what is not possible to do for stationary time series. The considered problems include
homogeneity testing (the so-called two sample problem)  clustering with respect to distribution
clustering with respect to independence  change point estimation  identity testing  and the
general problem of composite hypotheses testing. For the latter problem  a topological
criterion for the existence of a consistent test is presented. In addition  a number of open
problems is presented.

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