Statistical Inference in Inverse Problems with Qualitative Prior Information

在第一个资助期内，我们发展了统计逆回归模型中局部常数函数的渐近理论，并开始研究微观结构噪声模型中的路径波动率估计问题。在此基础上，我们将在第二个资助期结合并扩展这些方法，以获得波动率函数本身的形状约束置信带。为此，我们将在第一步开发反褶积问题的形状约束置信带。本项目将与L. d<s:1> mbgen [A1]， J. Woerner [B4]和A部分计量经济学组成员（E. Mammen [A3]， S. Sperlich [A4]， G. van den Berg [A7]）合作完成。我们的方法将用于分析以几秒的速率采样的FGBL高频滴答数据的现货波动。这将与M. Hoffmann （ENSAE Paris）合作完成。

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).