Statistical Inference in Inverse Problems with Qualitative Prior Information

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In the first funding period we have developed asymptotic theory for locally constant functions in statistical inverse regression models and have begun to investigate the problem of pathwise volatility estimation in microstructure noise models. Based on this work we will combine and extend these methods in the second funding period to obtain shape constrained confidence bands for the volatility function itself. To this end we will develop shape constrained confidence bands for deconvolution problems in a first step. This project will be performed in cooperation with L. Dümbgen [A1], J. Woerner [B4] and members of the econometrics group in part A (E. Mammen [A3], S. Sperlich [A4], G. van den Berg [A7]). Our methods will be used to analyse the spot volatility of FGBL high frequency tick data sampled at a rate of a few seconds. This will be done in cooperation with M. Hoffmann (ENSAE Paris).