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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 discuss inference on the Lévy measure in case of noisy observations. An extension of the pre-averaging method allows for a consistent estimation of the associated spectral function. The asymptotic behaviour of the novel estimator is the same as without noise. [Copyright &y& Elsevier]

Abstract: A lifetime with survival function , mean residual life function (MRL) , and finite mean is said to be new better than used in expectation (NBUE) if for all . We propose a new estimator for , based on a natural estimator of defined under the NBUE restriction. This is much simpler to implement than the only other restricted estimator in the literature. We also derive some asymptotic properties of the MRL of and extend our results to the censored case. [Copyright &y& Elsevier]

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: Multivariate measures of association are considered which, in the bivariate case, coincide with the population version of Spearman''s rho. For these measures, nonparametric estimators are introduced via the empirical copula. Their asymptotic normality is established under rather weak assumptions concerning the copula. The asymptotic variances are explicitly calculated for some copulas of simple structure. For general copulas, a nonparametric bootstrap is established. [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]

In this paper, we study the asymptotic distribution of the generally normalized maximum under finite mixture models. In one of the two theorems presented, we obtain a necessary and sufficient condition for this weak convergence, as well as the limit forms. The second theorem gives sufficient conditions for this convergence when the components of the mixture have different general normalizations. Examples are given to illustrate the applications of the two theorems. [Copyright &y& Elsevier]

This work deals with asymptotic properties of the [αm]th-order statistic of a type-II progressively censored sample of size m. Such an order statistic, indexed by α∈[0,1], is called the quantile process. Our main results concern the normalized version of the quantile process for which a weak convergence result is obtained. This result is applied in order to construct non-parametric estimators of quantiles. Monte-Carlo simulations illustrate the behavior of the estimators for limited sample size. [Copyright &y& Elsevier]