Titlebook: Dynamic Data Analysis; Modeling Data with D James Ramsay,Giles Hooker Book 2017 Springer Science+Business Media LLC 2017 functional data an

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Sozio?konomie und économie des conventionsarameter values and choose the ones which lead to best agreement with the data. Often, we need to search over both parameter values and initial conditions. This chapter introduces Gauss–Newton methods for minimizing a squared error criterion along with the sensitivity equations need to calculate der

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Die Einbettung der Sozio?konomiknon-parametric estimates of the state trajectory and its derivative. This allows the right hand side of the ODE to be fit to the estimated derivatives, which is often numerically easier than the trajectory matching described in Chap.?.. We discuss the ways in which this approach allows us to diagnos

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Dynamic Data Analysis978-1-4939-7190-9Series ISSN 0172-7397 Series E-ISSN 2197-568X

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Sarah Alexi,Friederike Heinzel,Uta MariniAutonomous nonlinear first order systems or single higher order nonlinear equations are expressible as

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Sarah Alexi,Friederike Heinzel,Uta MariniWithin the discipline of applied mathematics, a large part of dynamical systems theory is concerned with the description of the qualitative behavior of dynamical systems.

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Sozio?konomie und économie des conventionsWe have seen in the last chapter that linear differential equations can provide nice answers for a wide variety of problems, in the same way that multiple linear regression is the workhorse of applied statistics.

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Qualitative Behavior,Within the discipline of applied mathematics, a large part of dynamical systems theory is concerned with the description of the qualitative behavior of dynamical systems.

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Profiled Estimation for Linear Systems Estimated by Least Squares Fitting,We now describe an approach to parameter estimation and statistical inference called . or . that combines the virtues of both the nonlinear least squares method or trajectory matching described in Chap.?. and the gradient matching approach in Chap.?., but in a way that avoids the disadvantages of both.