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Barbara Szyszkowicz - An interplay of weighted approximations and change-point analysis



BARBARA SZYSZKOWICZ, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario  K1S 5B6, Canada
An interplay of weighted approximations and change-point analysis


When studying change-point problems, weighted partial sum-type processes frequently appear as the natural outcome of some nonparametric as well as parametric considerations. We present how approximation methods can lead to obtaining convergence results for such processes and to some ``unexpected'' results for their sup-functionals. Results and methods of strong and weak approximations have become an integral part of the theory and applications of probability and statistics in the last 40 or so years. Recent contributions in this area are mainly concerned with weighted approximations of stochastic processes based on ${\rm i.i.d.}$ observations (cf., e.g., M. Csörgo and L. Horváth, Weighted Approximations in Probability and Statistics, Wiley 1993). We construct tools for use in weighted approximations of additive processes in various metrics under ${\rm i.i.d.}$ sampling and combine these techniques with Le Cam's theory of contiguous measures. An appropriate parametrization of contiguity enables us to quantize a possible change from ${\rm i.i.d.}$ sampling to small disturbances afterwards in large sets of chronologically ordered data. Constructed new tools allow us to obtain results under the most stringent conditions.


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