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Two-step estimation of ordinary differential equation (ODE) is investigated when the transformation parameter is unknown. First we build the transformation parameter estimator by profile M-estimation. Then with a new consistency result of M-estimator, two-step estimator is proved to be consistent. Numerical studies validate the effectiveness of the proposed estimator. [ABSTRACT FROM AUTHOR]

The weak convergence of posterior distributions conditional on maximum pseudo-likelihood estimates (MPLE) is studied and exploited to justify the use of MPLE as summary statistics in approximate Bayesian computation (ABC). Our study could be generalized by replacing the pseudo-likelihood by other estimating functions (e.g. quasi-likelihoods and contrasts). [ABSTRACT FROM AUTHOR]

Abstract: We study the problem of parameter estimation for the continuous state branching processes with immigration, observed at discrete time points. The weighted conditional least square estimators (WCLSEs) are used for the drift parameters. Under the proper moment conditions, asymptotic distributions of the WCLSEs are obtained in the supercritical, sub- or critical cases. [Copyright &y& Elsevier]

Abstract: We consider a sequence of stochastic processes on converging weakly to X and call it polynomially convergent, if for continuous functionals F of polynomial growth. We present a sufficient moment conditions on for polynomial convergence and provide several examples, e.g. discrete excursions and depth first path associated to Galton–Watson trees. This concept leads to a new approach to moments of functionals of rooted trees such as height and path length. [Copyright &y& Elsevier]