DEMR embedded models in density saddlepoint approximations

In this paper we review the small asymptotic theory, particularly, the saddlepoint approximation to the density of sample mean and M-estimator. Furthermore, we merge the univariate differential equation motivated regression model, abbreviated as DEMR model, into small sample asymptotic theory, which is called saddlepoint approximation with embedded DEMR model. Two cases are briefly considered: DEMR embedded as a mean, and DEMR embedded as an M-estimator, with or without the knowledge of underlying distribution function from which the observation data sampled.