Handbook

The course presents the basic techniques of resampling methods useful in statistics. These have grown very popular over the last two decades as they offer reliable alternatives to traditional asymptotic approaches, mostly based on Central Limit Theorems. The flagship instance of resampling-based approaches is the so-called `bootstrap', by now considered as a real breakthrough in statistics. A very versatile technique, the bootstrap allows easy determination of the sampling distribution of any statistic of interest (estimator or test statistic) in a variety of situations. In fact, the bootstrap bypasses heavy analytical developments by substituting appropriate simulations. In many cases, the quality of the bootstrap approximation is better than its asymptotic counterparts, while in other situations, there is no asymptotic approximation available and the bootstrap turns out to be the only possibility for statistical inference. In this course, the bootstrap and other related resampling methods are first introduced in a general framework and their theoretical properties are investigated. Then, they are illustrated through many standard problems of statistical inference and common questions in related fields.