An Introduction to Bootstrap Methods with Applications to R

7

CHAPTER SPECIAL TOPICS

This chapter deals with a variety of statistical problems that can be effectively handled by the bootstrap. The only common theme is that the problems are complex. In many cases, classical approaches require special (restrictive) assumptions or provide incomplete or inadequate answers.

Although the bootstrap works well in these cases, theoretical justification is not always available, and just like with the error rate estimation problem, we rely on simulation studies. Efron and others felt that, although the bootstrap works well in simple problems and can be justified theoretically, it would be with the complex and intractable problems where it would have its biggest payoff.

7.1 SPATIAL DATA

7.1.1 Kriging

There are many applications of kriging, which is a technique that takes data at certain grid point in a region and generates a smooth two-dimensional curve to estimate the level of the measured variable at places between the observed values. So it is a form of spatial interpolation and is the most common way to fit such surfaces. In many applications, the measurements are taken over time. Sometimes the temporal element is important, and then spatial—temporal models are sought. We will not deal with those models in this text. Kriging is a procedure done at a fixed point in time. The surface can be generated by the method at several points in time.

Graphically, the surface is pictured as contours of constant level for the measured data. A video could be ...