PARAMETRIC ESTIMATION OF THE BASIS OF DISCRETIZED REALIZATIONS FROM A FINITE MARKOV CHAIN ON CONTINUOUS TIME

摘要

In this paper, we study the problem of estimation of 8 on the basis of a discretized sample, both when (a) the observations are taken at fixed intervals, and (b) at random intervals, of time. Even though the estimates of 0 based on these discretized samples are not directly comparable with that obtained from a continuous sample (since these refer to different samples), one can study, to some extent, the relative merits of different sampling designs by comparing the information contents of these samples. If the continuous inspection of the process cannot be made at all, the justification for using a suitable discretized observational plan is obvious;but even if it were possible to observe the process continuously, it may, in certain circumstances, be worthwhile using a discretized sample by choice.