Ebook Download | Probability for Statisticians | Galen Shorack is a statistics professor at the University of Washington. He specializes in empirical processes and probability theory. He and Wellner wrote a mammoth treatise on empirical processes that was well received. This book is very well written. It covers the basics for a standard advanced probability course very well. What sets it apart from most of its competition is its emphasis on applications to statistical inference.
Probability theory and empirical process theory in particular, are useful in proving consistency results about the bootstrap. So it is therefore no surprise that the bootstrap is covered in this book. Shorack provides a very lucid introduction to bootstrapping and on page 432 covers both the bootstrap principle and the weak bootstrap principle. In cases where the bootstrap principle can be verified, we are assured that the Monte Carlo approximation to the bootstrap works with probability one (i.e. it can only fail for data sets with zero probability of occurrence, fails on sets of probability measure zero in the jargon of probabilists). The practical implications of this is that you can apply it to the particular data set that you use the bootstrap on. The weak bootstrap applies a weaker convergence concept and is less useful because it only guarantees that the Monte Carlo approximation will work on most data sets that are drawn at random from a population with distribution F. It is less desirable because it provides no guarantee for the particular data set that you actually draw!
Probability theory and empirical process theory in particular, are useful in proving consistency results about the bootstrap. So it is therefore no surprise that the bootstrap is covered in this book. Shorack provides a very lucid introduction to bootstrapping and on page 432 covers both the bootstrap principle and the weak bootstrap principle. In cases where the bootstrap principle can be verified, we are assured that the Monte Carlo approximation to the bootstrap works with probability one (i.e. it can only fail for data sets with zero probability of occurrence, fails on sets of probability measure zero in the jargon of probabilists). The practical implications of this is that you can apply it to the particular data set that you use the bootstrap on. The weak bootstrap applies a weaker convergence concept and is less useful because it only guarantees that the Monte Carlo approximation will work on most data sets that are drawn at random from a population with distribution F. It is less desirable because it provides no guarantee for the particular data set that you actually draw!
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