84 research outputs found

    Strong Consistency of the Least-Squares Estimator in Simple Regression Models with Stochastic Regressors

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    Strong consistency of least squares estimators of the slope parameter in simple linear regression models is established for predetermined stochastic regressors. The main result covers a class of models which falls outside the applicability of what is presently available in the literature. An application to the identification of economic models with adaptive learning is discussed

    Consistent estimation of structural parameters in regression models with adaptive learning

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    In this paper we consider regression models with forecast feedback. Agents' expectations are formed via the recursive estimation of the parameters in an auxiliary model. The learning scheme employed by the agents belongs to the class of stochastic approximation algorithms whose gain sequence is decreasing to zero. Our focus is on the estimation of the parameters in the resulting actual law of motion. For a special case we show that the ordinary least squares estimator is consistent

    Estimating Structural Parameters in Regression Models with Adaptive Learning

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    This paper investigates the asymptotic properties of the ordinary least squares (OLS) estimator of structural parameters in a stylised macroeconomic model in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. In particular, when the learning recursion is subject to so-called decreasing gain sequences the model does not satisfy, in general, any of the sufficient conditions for consistent estimability available in the literature. The paper demonstrates that, for appropriate parameter sets, the OLS estimator nevertheless remains strongly consistent and asymptotically normally distributed

    A First and Second Law for Nonequilibrium Thermodynamics: Maximum Entropy Derivation of the Fluctuation-Dissipation Theorem and Entropy Production Functionals

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    A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory, we add constraints on the transition probability distribution which lead to a path probability of the Onsager-Machlup form. Additional constraints derived from energy and momentum conservation laws then introduce heat exchange and external driving forces into the system, with Lagrange multipliers related to the temperature and pressure of an external thermostatic system. The result is a fully time-dependent, non-local description of a nonequilibrium ensemble. Detailed accounting of the energy exchange and the change in information entropy of the central system then provides a description of the entropy production which is not dependent on the specification or existence of a steady-state or on any definition of thermostatic variables for the central system. These results are connected to the literature by showing a method for path re-weighting, creation of arbitrary fluctuation theorems, and by providing a simple derivation of Jarzynski relations referencing a steady-state. In addition, we identify path free energy and entropy (caliber) functionals which generate a first law of nonequilibrium thermodynamics by relating changes in the driving forces to changes in path averages. Analogous to the Gibbs relations, the variations in the path averages yield fluctuation-dissipation theorems. The thermodynamic entropy production can also be stated in terms of the caliber functional, resulting in a simple proof of our microscopic form for the Clausius statement. We find that the maximum entropy route provides a clear derivation of the path free energy functional, path-integral, Langevin, Brownian, and Fokker-Planck statements of nonequilibrium processes.Comment: 35 page

    Protein Aggregation and Protein Instability Govern Familial Amyotrophic Lateral Sclerosis Patient Survival

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    The nature of the “toxic gain of function” that results from amyotrophic lateral sclerosis (ALS)-, Parkinson-, and Alzheimer-related mutations is a matter of debate. As a result no adequate model of any neurodegenerative disease etiology exists. We demonstrate that two synergistic properties, namely, increased protein aggregation propensity (increased likelihood that an unfolded protein will aggregate) and decreased protein stability (increased likelihood that a protein will unfold), are central to ALS etiology. Taken together these properties account for 69% of the variability in mutant Cu/Zn-superoxide-dismutase-linked familial ALS patient survival times. Aggregation is a concentration-dependent process, and spinal cord motor neurons have higher concentrations of Cu/Zn-superoxide dismutase than the surrounding cells. Protein aggregation therefore is expected to contribute to the selective vulnerability of motor neurons in familial ALS

    Strong consistency of least squares estimators in the monotone regression model

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    SIGLEBibliothek Weltwirtschaft Kiel C117,312 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

    A Note on an Estimation Problem in Models with Adaptive Learning

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