Statistical Inference in Inverse Problems with Qualitative Prior Information

具有定性先验信息的反问题中的统计推断

• 批准号: 69240132
• 负责人: Professor Dr. Axel Munk
• 金额: --
• 依托单位: Institut für Mathematische Stochastik (IMS)
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/69240132?language=en
• 关键词: Statistical; Inference; Inverse; Problems; Qualitative

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).

在第一个资助期内，我们已经开发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。基于这项工作，我们将联合收割机，并在第二个融资期扩展这些方法，以获得形状约束的波动率函数本身的置信带。为此，我们将制定形状约束的置信带反卷积问题的第一步。该项目将与L. Dümbgen [A1]，J. Woerner [B4]和计量经济学小组的成员在A部分（E. Mammen [A3]，S. Sperlich [A4]，G.货车登贝格[A7]）。我们的方法将被用来分析以几秒钟的速度采样的FGBL高频报价数据的现货波动率。这将与M。霍夫曼（ENSAE巴黎）。