Bootstrap Techniques in the Partial Linear Model

Abstract

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.