EMPIRICAL LIKELIHOOD ESTIMATORS OF THE LINEAR SIMULTANEOUS EQUATIONS MODEL

Information theoretic estimators are specified for a system of linear simultaneous equations, including maximum empirical likelihood, maximum empirical exponential likelihood, and maximum log Euclidean likelihood. Monte Carlo experiments are used to compare finite sample performance of these estimators to traditional generalized method of moments.Research Methods/ Statistical Methods,

A STRUCTURAL-EQUATION GME ESTIMATOR

A generalized maximum entropy estimator is developed for the linear simultaneous equations systems model. We provide results on large and small sample properties of the estimator. Empirical results illustrate efficiency advantages of the generalized maximum entropy estimator proposed in this study over traditional estimators (e.g., 2SLS and 3SLS).Research Methods/ Statistical Methods,

INFORMATION THEORETIC ALTERNATIVES TO TRADITIONAL SIMULTANEOUS EQUATIONS ESTIMATORS IN THE PRESENCE OF HETEROSKEDASTICITY

Finite sampling properties of information theoretic estimators of the simultaneous equations model, including maximum empirical likelihood, maximum empirical exponential likelihood, and maximum log Euclidean likelihood, are examined in the presence of selected forms of heteroskedasticity. Extensive Monte Carlo experiments are used to compare finite sample performance of Wald, Likelihood ratio, and Lagrangian multiplier tests constructed from information theoretic estimators to those from traditional generalized method of moments.Research Methods/ Statistical Methods,

Deformation of a flexible polymer in a random flow with long correlation time

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and FENE dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil-stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.Comment: 10 page

Thermodynamic anomalies in a lattice model of water

We investigate a lattice-fluid model of water, defined on a three-dimensional body centered cubic lattice. Model molecules possess a tetrahedral symmetry, with four equivalent bonding arms, aiming to mimic the formation of hydrogen bonds. The model is similar to the one proposed by Roberts and Debenedetti [J. Chem. Phys. 105, 658 (1996)], simplified in that no distinction between bond "donors" and "acceptors" is imposed. Bond formation depends both on orientation and local density. In the ground state, we show that two different ordered (ice) phases are allowed. At finite temperature, we analyze homogeneous phases only, working out phase diagram, response functions, the temperature of maximum density locus, and the Kauzmann line. We make use of a generalized first order approximation on a tetrahedral cluster. In the liquid phase, the model exhibits several anomalous properties observed in real water. In the low temperature region (supercooled liquid), there are evidences of a second critical point and, for some range of parameter values, this scenario is compatible with the existence of a reentrant spinodal.Comment: 12 pages, 9 figures, 1 tabl

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions -- generalizations of these are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner's theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired

A first--order irreversible thermodynamic approach to a simple energy converter

Several authors have shown that dissipative thermal cycle models based on Finite-Time Thermodynamics exhibit loop-shaped curves of power output versus efficiency, such as it occurs with actual dissipative thermal engines. Within the context of First-Order Irreversible Thermodynamics (FOIT), in this work we show that for an energy converter consisting of two coupled fluxes it is also possible to find loop-shaped curves of both power output and the so-called ecological function against efficiency. In a previous work Stucki [J.W. Stucki, Eur. J. Biochem. vol. 109, 269 (1980)] used a FOIT-approach to describe the modes of thermodynamic performance of oxidative phosphorylation involved in ATP-synthesis within mithochondrias. In that work the author did not use the mentioned loop-shaped curves and he proposed that oxidative phosphorylation operates in a steady state simultaneously at minimum entropy production and maximum efficiency, by means of a conductance matching condition between extreme states of zero and infinite conductances respectively. In the present work we show that all Stucki's results about the oxidative phosphorylation energetics can be obtained without the so-called conductance matching condition. On the other hand, we also show that the minimum entropy production state implies both null power output and efficiency and therefore this state is not fulfilled by the oxidative phosphorylation performance. Our results suggest that actual efficiency values of oxidative phosphorylation performance are better described by a mode of operation consisting in the simultaneous maximization of the so-called ecological function and the efficiency.Comment: 20 pages, 7 figures, submitted to Phys. Rev.

A BAYESIAN ALTERNATIVE TO GENERALIZED CROSS ENTROPY SOLUTIONS FOR UNDERDETERMINED ECONOMETRIC MODELS

This paper presents a Bayesian alternative to Generalized Maximum Entropy (GME) and Generalized Cross Entropy (GCE) methods for deriving solutions to econometric models represented by underdetermined systems of equations. For certain types of econometric model specifications, the Bayesian approach provides fully equivalent results to GME-GCE techniques. However, in its general form, the proposed Bayesian methodology allows a more direct and straightforwardly interpretable formulation of available prior information and can reduce significantly the computational effort involved in finding solutions. The technique can be adapted to provide solutions in situations characterized by either informative or uninformative prior information.Underdetermined Equation Systems, Maximum Entropy, Bayesian Priors, Structural Estimation, Calibration, Research Methods/ Statistical Methods, C11, C13, C51,