Some Applications of Wavelets in Statistics

该项目扩展了P.I.研究和教育的新方向。该项目旨在开发小波方法，并将其用于跨学科研究工作。韦夫特那个私家侦探的博士学位。自从Daubechies和Mallat于1989年发现了正交小波基以来，小波基在许多科学领域中变得越来越受欢迎。私家侦探。在未来五年中，他将致力于研究小波方法在四个不同但相互关联的领域中的应用：i）非参数密度估计;ii）时间序列;iii）曲线回归中的降维; iv）生物学中的跨学科研究。贝叶斯小波分量选择技术，最后，小波方法在蛋白质和基因组分析中的应用。将开设一门关于小波方法的课程。理论将与实际兴趣的许多领域的应用和讲座与计算机演示相结合。该课程将在高级研究生水平，为统计学和非统计学专业。我们的目标将是培养学生，随后可以做他们的论文工作小波。本课程还将培养学生在统计学以外的研究领域运用小波方法的能力。

This project extends current interests of the P.I. in new directions, in both research and education. The project aims at the development of wavelet methods as well as at their use in interdisciplinary research efforts. Wavelets, the P.I.'s Ph.D. thesis subject, have become increasingly popular in many scientific fields since the discovery of orthonormal wavelet bases byDaubechies and Mallat in 1989. The work that the P.I. intends to do over the next five years addresses the application of wavelet methods in four different but interrelated areas:i) nonparametric density estimation;ii) time series;iii) dimension reduction in curve regression, andiv) interdisciplinary research in biology.Specific contributions include the development of nonparametric wavelet-based hypothesis tests; the wavelet estimation of parameters of random processes, with emphasis on long-memory; Bayesian wavelet component selection techniques and, finally, applications of waveletmethods in the analysis of proteins and genomes.In addition to the research component, the P.I. will develop a course on wavelet methods. Theory will be interlaced with applications in many areas of practical interest and lectures integrated with computer demonstrations. The course will be at the advanced graduate level, for statisticsand non-statistics majors. The goal will be to train students that may subsequently do their dissertation work on wavelets. The course will also produce students capable of bringingwavelet methods in research fields other than statistics.