Computer-intensive rate estimation, diverging statistics and scanning

Computer-intensive rate estimation, diverging statistics, and scanning

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown to be accurate in a very general setting without requiring the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extract...

Computer Intensive Statistics 1. Introduction

The principle aim of these notes is to provide context and motivation for the APTS Computer Intensive Statistics Module and to make the module as self-contained as is feasible. Statistics is a broad discipline and the APTS cohort naturally has a diverse range of backgrounds. If you have attended the earlier APTS modules this year, especially Statistical Computing and Statistical Inference, then...

False discovery rate for scanning statistics

The false discovery rate is a criterion for controlling Type I error in simultaneous testing of multiple hypotheses. For scanning statistics, due to local dependence, clusters of neighbouring hypotheses are likely to be rejected together. In such situations, it is more intuitive and informative to group neighbouring rejections together and count them as a single discovery, with the false discov...

Diverging moments and parameter estimation

Heavy tailed distributions which allow for values far from the mean to occur with considerable probability are of increasing importance in various applications as the arsenal of analytical and numerical tools grows. Examples of interest are the Stable and more generally the Pareto distributions for which moments of sufficiently large order diverge. In fact, the asymptotic powerlaws of the distr...

Computer Intensive Methods