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  • 1
    ISSN: 1573-2738
    Keywords: fuzzy constraint method ; multiple scales ; non-equilibrium statistical thermodynamics ; polymers ; unified relaxation spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The molecular relaxation mechanisms of polymers withmulti-scale units of motion in glassy, rubbery and melt states areproposed based upon a fuzzy constraint method and non-equilibriumstatistical thermodynamics. The entanglement effects due to cohesiveforce and steric hindrance are expressed quantitatively in terms of amembership function. The micro-Brownian motion of a polymer chain isgoverned by the Langevin equation, which accounts for viscous force,nonuniform tension, entanglement constraint force and random force.Perturbation solutions have been established for different time and sizescales. The solutions account for the effects of both intramolecular andintermolecular interactions in the relaxation process. The unifiedrelaxation spectrum over many orders of time scale is a naturalconsequence of macromolecular structure, which satisfies thetime-temperature equivalence in the form of the Arrhenius equation atlow and high temperatures and in the form of the WLF equation near theglass transition temperature. The barrier model, the normal mode theory,the retraction and reptation theories can be taken as special casescorresponding to different scales.
    Type of Medium: Electronic Resource
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  • 2
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a pre-asymptotic sieve variance estimator that captures temporal dependence. We construct a pre-asymptotic Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled pre-asymptotic Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled pre-asymptotic Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.
    Keywords: ddc:330 ; Weak Dependence ; Sieve M Estimation ; Sieve Riesz Representor ; Irregular Functional ; Misspecification ; Pre-asymptotic Variance ; Orthogonal Series Long Run Variance Estimation ; F Distribution
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:workingPaper
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  • 3
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the already-well-known parametric literature. This means that for computational purposes, an empirical researcher can ignore the semiparametric nature of the problem and do all calculations as if it were a parametric situation. We hope that this simplicity will promote the use of semiparametric procedures.
    Keywords: C14 ; ddc:330 ; Nichtparametrisches Verfahren
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 4
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these principal components. We also characterize the limiting behavior of the associated eigenvalues, the objects used to quantify the incremental importance of the principal components. By exploiting the theory of continuous-time, reversible Markov processes, we give a different interpretation of the principal components and the smoothness constraints. When the diffusion matrix is used to enforce smoothness, the principal components maximize long-run variation relative to the overall variation subject to orthogonality constraints. Moreover, the principal components behave as scalar autoregressions with heteroskedastic innovations. Finally, we explore implications for a more general class of stationary, multivariate diffusion processes.
    Keywords: ddc:330 ; Multivariate Analyse ; Markovscher Prozess ; Theorie
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 5
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We also consider a semiparametric habit-based, consumption capital asset pricing model. There we find the rank condition is implied by an integral equation of the second kind having a one-dimensional null space.
    Keywords: C12 ; C13 ; C23 ; ddc:330 ; Identification ; Local Identification ; Nonparametric Models ; Asset Pricing ; Finanzmarkt ; Capital Asset Pricing Model
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 6
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction models with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables. Our bound results are applicable to semiparametric panel data models and semiparametric two stage plug-in problems. As an example, we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables (IV) regression, and find that the simple plug-in estimator is not efficient. Finally, we present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric efficiency bound.
    Keywords: C14 ; C22 ; ddc:330 ; Sequential moment models ; Semiparametric efficiency bounds ; Optimally weighted orthogonalized sieve minimum distance ; Nonparametric IV regression ; Weighted average derivatives ; Partially linear quantile IV ; Nichtparametrisches Verfahren ; Sequentialanalyse ; Momentenmethode ; Theorie
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 7
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are identified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important applications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.
    Keywords: C13 ; C14 ; D12 ; ddc:330 ; nonsmooth residuals ; nonlinear ill-posed inverse ; penalized sieve minimum distance ; modulus of continuity ; average derivative of a nonparametric nonlinear IV regression ; nonparametric additive quantile IV regression ; Schätztheorie ; Nichtparametrisches Verfahren ; Regression ; Momentenmethode
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 8
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of √ n-consistent estimators whose cardinality increases with sample size. A special case of our framework corresponds to the conditional moment restriction and the implied estimator in that case is shown to achieve the semiparametric efficiency bound. The proofs do not rely on smoothness of underlying criterion functions.
    Keywords: C12 ; C13 ; C14 ; ddc:330 ; Instrumental Variables ; Minimum Distance ; Semiparametric Efficiency ; Two-Stage Least Squares
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 9
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.
    Keywords: C13 ; C14 ; C20 ; ddc:330 ; Nonlinear time series ; Temporal dependence ; Tail dependence ; Penalized sieve M estimation ; Penalized sieve minimum distance ; Semiparametric two-step ; Nonlinear ill-posed inverse ; Mixtures ; Conditional moment restrictions ; Nonparametric endogeneity ; Dynamic asset pricing ; Varying coefficient VAR ; GARCH ; Copulas ; Value-at-risk ; Zeitreihenanalyse ; Nichtparametrisches Verfahren ; VAR-Modell ; ARCH-Modell
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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  • 10
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    London: Centre for Microdata Methods and Practice (cemmap)
    Publication Date: 2014-09-08
    Description: This paper considers efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant distributions and parametric copula functions; where the copulas capture all scale-free temporal dependence and tail dependence of the processes. The Markov models generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that Markov processes generated via Clayton, Gumbel and Student's t copulas (with tail dependence) are all geometric ergodic. We then propose a sieve maximum likelihood estimation (MLE) for the copula parameter, the invariant distribution and the conditional quantiles. We show that the sieve MLEs of any smooth functionals are root-n consistent, asymptotically normal and efficient; and that the sieve likelihood ratio statistics is chi-square distributed. We present Monte Carlo studies to compare the finite sample performance of the sieve MLE, the two-step estimator of Chen and Fan (2006), the correctly specified parametric MLE and the incorrectly specified parametric MLE. The simulation results indicate that our sieve MLEs perform very well; having much smaller biases and smaller variances than the two-step estimator for Markov models generated by Clayton, Gumbel and other copulas having strong tail dependence
    Keywords: C14 ; C22 ; ddc:330 ; Copula ; Tail dependence ; Nonlinear Markov models ; Geometric ergodicity ; Sieve MLE ; Semiparametric efficiency ; Sieve likelihood ratio statistics ; Value-at-Risk ; Kopula (Mathematik) ; Markovscher Prozess ; Nichtparametrisches Verfahren ; Risikomaß ; Zeitreihenanalyse ; Theorie
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
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