Heyman, Megan2016-08-192016-08-192016-04https://hdl.handle.net/11299/181739University of Minnesota Ph.D. dissertation. April 2016. Major: Statistics. Advisor: Snigdhansu Chatterjee. 1 computer file (PDF); xi, 233 pages.As a tree grows, the trunk diameter increases, and in a typical year, a tree-ring is produced. The width of this ring reflects growing conditions during the year -- when standardized, a wider ring indicates better growing conditions. Thus, tree-rings contain yearly climatic information, such as precipitation and temperature. Tree-ring records exist for thousands of years in many locations across the earth, and a goal of paleoclimatologists is to use these records to understand past climate. A subset of records from the international tree-ring data bank (ITRDB) for Pinus ponderosa is introduced and analyzed in this talk. We specifically address what significant signals (long or short term) are included in this chronology. A newly proposed resampling technique, called the wild scale-enhanced bootstrap (WiSE bootstrap), is utilized in this analysis and implemented using the WiSEBoot R package. This methodology is based in a partial linear model where the nonparametric component is approximated by a wavelet basis. The WiSE bootstrap provides a model selection (in the basis dimension) and consistent parameter estimates. Additionally, the document includes an overview of all of our research results involving the partial linear model, bootstrap, and wavelets.enbootstrapclimatepartial linear modelwaveletsThesis or Dissertation