Numerical Computation of the Small Balls Probability for RandomFunctions with Normal Components

Abstract

Statistical methods are often based on the properties of the distribution of random variables or randomvectors. In functional data analysis (FDA) we do not work with random observation containing a finite randomvector, but the whole function is one observation. We call it the functional random variable or the randomfunction, in short. This paper offers the possibility to generate random functions with normal components. In thiscase, the probability of small balls can be calculated numerically using the characteristic function. This tool canbe very useful in simulations and testing various kinds of estimates.