Eigenvalues Of A Fredholm Integral Operator And Applications To Problems Of Statistical Inference

Abstract

. We determine the eigenvalues of a Fredholm integral operator of the second kind. The solution of the eigenvalue problem has applications to finding the distribution function of a stochastic integral. The stochastic integral itself represents the asymptotic form of a statistical test. Also discussed are related results for inference and applications. 1. Introduction. Applications of Fredholm integral operators in the areas of physical sciences and engineering are well known. Their applications to problems of statistical inference are probably less known among researchers in mathematics and other disciplines. The dynamic instability inherent in physical processes can often be statistically modelled by the change-point method. The change-point problem primarily consists of testing for a model with no change in the model parameters against a model where parameter changes occur after a certain unknown point of time. The problem has received wide attention among researchers in statistical ..