Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications

Chapter 7 considers selection of block size, beginning with the theory of MSE-optimal selections and continuing with subsampling and jackknife-afterbootstrap procedures. Chapter 8 presents model-based bootstrap methods for dealing with stationary, explosive, and unstable autoregressive processes, concluding with adaptations to stationary ARMA models. Chapter 9 introduces a transformation-based bootstrap for linear processes focused on resampling of the discrete Fourier transforms of the data. Chapter 10 addresses processes exhibiting long-range dependence, stepping through MBB and subsampling approaches. Chapter 11 provides results on bootstrapping heavy-tailed time series and on bootstraping maxima and minima of stationary processes. Chapter 12 concludes the volume with a study of bootstrap methods in spatial data analysis, including regularly and irregularly spaced sampling processes and methods of prediction in spatial contexts. Overall, this is a well-produced book, with excellent technical typesetting of the intensely formal material. Comparative simulation results are often presented suboptimally: Figure 4.2 is an example in which MBB, NBB, CBB, and SB procedure results are illustrated using juxtaposed histograms. Superimposed density estimates would be more efficient and informative. Figures 5.1 and 5.2 include undefined notation in keys and use a single line type for functions with intersecting trajectories. These shortcomings are not too serious, but I mention them to remind statisticians of the appropriateness and feasibility of achieving the highest standards of data visualization, even in chiefly theoretical contexts. It is also worth reflecting on the term “dependent data” used in the title. Although it is true that the coverage of spatial data analysis frees the author from limiting the title to mention of time series, there are many other types of dependent data for which research on bootstrap methods exists: panel, longitudinal, and familial study designs give rise to such data. These are not directly addressed in this monograph. In summary, Resampling Methods for Dependent Data is an impressive compendium of results on an important topic, compiled and exposited by a major contributor to the field. For related reading, I refer you to the review journal Statistical Science (vol. 18, no. 2), which celebrates the twenty-fifth anniversary of the bootstrap, with a collection of articles on theoretical impacts and on topic-specific impacts in such fields as sample surveys, econometrics, and time series analysis. One article in particular (Politis 2003) provides a very compact current review of the area.