Using Bootstrap to Increase Data in Predictive Analytics with Extreme Value Distribution

Abstract

The bootstrap is one of the method of studying statistical math which this article uses it but is a major tool for studying and evaluating the values of parameters in probability distribution. Overview of the theory of infinite distribution functions. The tool to deal with the problems raised in the paper is the mathematical methods of random analysis by theory of random process and multivariate statistics. Observations (realisations of a stationary process) are not independent, but dependence in time series is relatively simple example of dependent data. Through a simulation study we found that the pseudo data generated from the bootstrap method always showed a weaker dependence among the observations than the time series they were sampled from, hence we can draw the conclusion that even by re-sampling blocks instead of single observations we will lose some of structural from of the original sample. A potential difficulty by the using of likelihood methods for the GEV concerns the regularity conditions that are required for the usual asymptotic properties associated with the maximum likelihood estimator to be valid. To estimate the value of a parameter in GEV we can use classical methods of mathematical statistics such as the maximum likelihood method or the least squares method, but they all require a certain number samples for verification. For the bootstrap method, this is obviously not needed; here we use the limit theorems of probability theory and multivariate statistics to solve the problem even if there is only one sample data. That is the important practical significance that our paper wants to convey. In predictive analysis problems, in case the actual data is incomplete, not long enough, we can use bootstrap to add data.