Statistical Inference for Some Special Families of Stochastic Processes

Publisher Summary This chapter presents statistical inference for some special families of stochastic processes. Many of the classical univariate inferential techniques for means are valid exactly or in a modified form for larger parameter spaces. To fit a wide variety of data, retaining the sample function space of the Wiener process is important. The data can also be fitted by enlarging the parameter space by placing a mixing measure—the variance parameter of the Wiener process. The chapter describes distribution theory. A stochastic process is called spherically exchangeable (S-E) if a function ψ exists there on the positive half line such that for each finite set of natural numbers, the joint characteristic function of the so-numbered Xs satisfies. Each S-E process is a variance mixture of Gaussian processes.