Nonparametric Predictive Methods for Bootstrap and Test Reproducibility
PDF Accepted Version
783KbAbstractThis thesis investigates a new bootstrap method, this method is called Nonparametric Predictive Inference Bootstrap (NPI B). Nonparametric predictive inference (NPI) is a frequentist statistics approach that makes few assumptions, enabled by using lower and upper probabilities to quantify uncertainty, and explicitly focuses on future observations. In the NPI B method, we use a sample of n observations to create n + 1 intervals and draw one future value uniformly from one interval. Then this value is added to the data and the process is repeated, now with n+1 observations. Repetition of this process leads to the NPI B sample, which therefore is not taken from the actual sample, but hermes clutch bag replica black
consists of values in the whole range of possible observations, also going beyond the range of the actual sample. We explore NPI B for data on finite intervals, real line and non negative observations, and compare it to other bootstrap methods via simulation studies which show that the NPI B method works well as a prediction method. The NPI method is presented for the reproducibility probability (RP) of some nonparametric tests. Recently, there has been substantial interest in the reproducibility probability, where not only its estimation but also its actual definition and interpretation are not uniquely determined in the classical frequentist statistics framework. The explicitly predictive nature of NPI provides a natural formulation of inferences on RP. It is used to derive lower and upper bounds of RP values (known as the NPI RP method) but if we consider large sample sizes, the computation of these bounds is difficult. We explore the NPI B method to predict the RP values (they are called NPI B RP values) of some nonparametric tests. Reproducibility of tests is an important characteristic of the practical relevance of test outcomes.