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Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.


Papers
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Journal ArticleDOI
TL;DR: These observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance in an inverted pendulum with time-delayed feedback.
Abstract: Motion analysis in three dimensions demonstrate that the fluctuations in the vertical displacement angle of a stick balanced at the fingertip obey a scaling law characteristic of on-off intermittency and that >98% of the corrective movements occur fast compared to the measured time delay. These experimental observations are reproduced by a model for an inverted pendulum with time-delayed feedback in which parametric noise forces a control parameter across a particular stability boundary. Our observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance.

344 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered a model class of second order, linear, parametric, elliptic PDE's in a bounded domain D with coefficients depending on possibly countably many parameters and showed that the dependence of the solution on the parameters in the diffusion coefficient is analytically smooth.
Abstract: Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochastic elliptic problems. This paper considers a model class of second order, linear, parametric, elliptic PDE's in a bounded domain D with coefficients depending on possibly countably many parameters. It shows that the dependence of the solution on the parameters in the diffusion coefficient is analytically smooth. This analyticity is then exploited to prove that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations can be simultaneously approximated by multivariate polynomials (in the parameters) with coefficients taking values in the Hilbert space of weak solutions of the elliptic problem with a controlled number of terms N. The convergence rate in terms of N does not depend on the number of parameters in V which may be countable, therefore breaking the curse of dimensionality. The discretization of the coefficients from a family of continuous, piecewise linear finite element functions in D is shown to yield finite dimensional approximations whose convergence rate in terms of the overall number Ndof of degrees of freedom is the minimum of the convergence rates afforded by the best N-term sequence approximations in the parameter space and the rate of finite element approximations in D for a single instance of the parametric problem.

342 citations

Journal ArticleDOI
TL;DR: In this article, the amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier, which is described by means of the time-dependent density operator for the system.
Abstract: The amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier. The statistical properties of the amplifier fields are described by means of the time-dependent density operator for the system. In doing this, extensive use is made of the coherent states and the $P$ representation of the density operator, which provide a quantum-mechanical description of the fields closely resembling their classical description. Explicit solutions are obtained for the density operator for either of the two field modes for a variety of initial states of the modes. Initial states considered include combinations of coherent states, chaotic mixtures, and $n$-quantum states. Particular attention is given the behavior of the amplifier fields in the limit of large amplification. The conditions are established under which the amplification process leads in this limit to the existence of a non-negative $P$ representation for the density operator for a single mode of oscillation.

339 citations

Posted Content
TL;DR: In this article, the authors proposed two new methods for conditional distribution estimation based on locally fitting a logistic model and an adjusted form of the Nadaraya-Watson estimator.
Abstract: Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya--Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.

339 citations

MonographDOI
TL;DR: In this article, the authors propose a non-parametric approach for estimating parametric models from state space models and nonlinear and non-stationary models, based on nonparametric models and parametric linearity tests.
Abstract: 1. Concepts, models and definitions 2. Nonlinear models in economic theory 3. Parametric nonlinear models 4. The nonparametric approach 5. Parametric linearity tests 6. Testing parameter constancy 7. Nonparametric specification tests 8. Conditional heteroskedasticity 9. State space models 10. Nonparametric models 11. Nonlinear and nonstationary models 12. Estimating parametric models 13. Basic nonparametric estimates 14. Forecasting from nonlinear models 15. Nonlinear impulse responses 16. Building nonlinear models 17. Other topics

339 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20252
20242
20233,966
20227,822
20211,968
20202,033