• The Bootstrapped Response Function

      Guiot, J.; Laboratoire de Botanique Historique & Palynologie, UA CNRS (Tree-Ring Society, 1991)
      The bootstrap procedure provides a way to test the significance of the regression coefficients and the stability of the estimates in response functions generated by regression on principal components. A subroutine RESBO, which calculates a bootstrapped response function, has been added to Fritts' program PRECON.
    • Identifying Low-Frequency Tree-Ring Variation

      Sheppard, Paul R.; Laboratory of Tree-Ring Research, University of Arizona, Tucson, Arizona (Tree-Ring Society, 1991)
      I propose an approach to provide 95% confidence intervals for a chronology of low-frequency tree-ring variation so that a level of significance or importance for trends can be inferred. The approach also visually reveals the portions of a chronology in which sample depth is so poor that low-frequency variation is not robustly estimated. A key characteristic of the approach is that it is essentially a reordering of the individual steps commonly used in constructing standard tree-ring chronologies; consequently, it is computationally simple for researchers who already routinely construct standard tree-ring chronologies. The most important ramification of the approach is that each year of the chronology has a distribution of smoothed index values with which to estimate confidence intervals around the chronology of low-frequency variation. It can be argued that the approach constitutes multiple significance testing of means, which causes the α level for the confidence interval to be unknown. Nonetheless, the approach is still useful in that it provides a way to evaluate the probable importance of low-frequency trends expressed in tree-ring chronologies.