While Monte Carlo methods for bootstrapping are typically easy to implement, they can be quite time intensive. This work aims to extend an established convolutional method of bootstrapping to work when convolutions in two or more dimensions are required. The convolutional method relies on efficient computational tools rather than Monte Carlo simulation which can greatly reduce the computation time. The proposed method is particularly well suited for the analysis of degradation data when the data are not collected on time intervals of equal length. The convolutional bootstrapping method is typically much faster than the Monte Carlo bootstrap and can be used to produce exact results in some simple cases. Even in more complicated applications, where it is not feasible to find exact results, mathematical bounds can be placed on the resulting distribution. With these benefits of the convolutional method, this bootstrapping approach has been shown to be a useful alternative to the traditional Monte Carlo bootstrap.
College and Department
Physical and Mathematical Sciences; Statistics
BYU ScholarsArchive Citation
Clark, Jared M., "A Multidimensional Convolutional Bootstrapping Method for the Analysis of Degradation Data" (2022). Theses and Dissertations. 9479.
Discrete Fourier Transform, Lévy Process, Monte Carlo Estimation, Saddlepoint Approximation