Maximal uniform convergence rates in parametric estimation problems

This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems

Non-isothermal decomposition kinetics of theobromine in nitrogen atmosphere

The non-isothermal decomposition process of theobromine under nitrogen atmosphere was studied using the differential thermal analysis (DTA), from room temperature up to 500 °C, at heating rates, 5, 15 and 20 °C/min. The results showed that theobromine decomposes in two steps. The kinetic analysis of the first decomposition step was performed using Kissinger, Friedman, Flynn-Wall-Ozawa, and Kissinger-Akahira-Sunose isoconventional methods. The kinetic model was determined using Šatava-Šesták method. Results showed that the non-isothermal decomposition mechanism of theobromine corresponds to nucleation and growth, following the Avrami-Erofeev equation. The forms of the integral and differential equations for the mechanism function are g(α)=(-ln(1-α))2/3 and f(α)=(3/2)(1-α)(-ln(1-α))1/3, respectively. Thermodynamic parameters of the non-isothermal decomposition process, change of enthalpy (ΔH), change of entropy (ΔS), and change of Gibbs free energy (ΔG) values were calculated

THE STRUCTURE OF THE ASSUMED MODEL THROUGH THE DISCRETIZED LIKELIHOOD ESTIMATOR

In the presence of a nuisance parameter the asymptotic deficiency of the discretizedlikelihood estimator (DLE) relative to the bias-adjusted maximum likelihood estimatoris obtained under the assumed model. It consists of two parts. One is the lossof information associated with the DLE of the parameter to be estimated. Another,is that due to the "incorrectness" of the assumed model. Some examples on the normaland Weibull type distributions are given