By J.O. Ramsay

ISBN-10: 0387224653

ISBN-13: 9780387224657

ISBN-10: 0387954147

ISBN-13: 9780387954141

ISBN-10: 0585472750

ISBN-13: 9780585472751

Useful facts research is a brand new region of statistical study, and the 2 authors of this name current the 1st number of tools in book-form. a lot of the paintings is unique to the authors. entrance subject; creation; existence path facts in Criminology; The Nondurable items Index; Bone Shapes from a Paleopathology examine; Modeling Reaction-Time Distributions; Zooming in on Human progress; Time Warping Handwriting and climate documents; How Do Bone Shapes point out Arthritis?; sensible versions for attempt goods; Predicting Lip Acceleration from Electromyography; The Dynamics of Handwriting published Characters; A Differential Equation for Juggling; again subject

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**Extra resources for Applied functional data analysis : methods and case studies**

**Sample text**

This leads us naturally to the idea of using a diﬀerential equation to describe the process, a type of modeling that will allow us to model the dynamic behavior seen in the phase-plane plot as well as the curve itself. We use diﬀerential equations in models in Chapters 11 and 12. 6. 1 Fourth derivative roughness penalties We can imagine that the economic forces generating the log index values are reasonably smooth. In practice, this means that a curve giving a satisfactory picture of these processes has a certain number of derivatives.

Then U −1 g (j) is the basis coeﬃcient vector of the jth smoothed principal component weight function. 6 Cross-validation for estimating the mean In classical univariate statistics, the mean of a distribution is the least squares predictor of observations from the distribution, in the sense that if µ is the population mean, and X is a random observation from the distribution, then E{(X − µ)2 } < E{(X − a)2 } for any other number a. So one way of evaluating an estimate of µ is to take a number of new observations from the distribution, and see how well they are predicted by the value yielded by our estimate.

These are intended for readers who are interested in the way that the basis expansions are used in practice and might wish to reconstruct the calculations for themselves. The algorithms are not explained in detail, but the more mathematically sophisticated reader not willing to take the results on trust should have no diﬃculty in reconstructing the arguments underlying them. 5. How are functions stored and processed? 15. A B-spline basis that can be used to represent smooth functions The ﬁrst step is to use discrete observations of a function to obtain a basis representation.

### Applied functional data analysis : methods and case studies by J.O. Ramsay

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