Chapter 8 - Large Sample Theory for Continuous Parameter Stochastic Processes

Abstract

This chapter presents a study of continuous parameter processes. Two approaches have been used up to now to study asymptotic theory of inference for continuous parameter processes. The first method consists of reduction of a continuous record of a process to a countable set of observable coordinates and then using some other methods. The second approach is to study the inference aspects using martingale theory. In contrast to the discrete parameter stochastic processes, the chapter highlights the additional problems of determining the right properties of the sample paths to be observed, finding a way of representing these observations and seeing whether the probability structure can be determined from these observations. The chapter discusses the problems of testing statistical hypotheses for continuous parameter stochastic processes. It is possible to transfer the ideas and methods of Neyman-Pearson theory to this case. It explains asymptotic theory of likelihood equation estimates for continuous parameter stochastic processes.