By Jim Ramsay, Giles Hooker

ISBN-10: 038740080X

ISBN-13: 9780387400808

This is often the second one variation of a hugely capable ebook which has bought approximately 3000 copies worldwide when you consider that its e-book in 1997. Many chapters might be rewritten and multiplied as a result of loads of development in those components because the e-book of the 1st variation. Bernard Silverman is the writer of 2 different books, every one of which has lifetime revenues of greater than 4000 copies. He has a good recognition either as a researcher and an writer. this can be more likely to be the bestselling ebook within the Springer sequence in records for a few years.

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**Extra resources for Functional Data Analysis (Springer Series in Statistics)**

**Example text**

We see that the mean force looks remarkably like a number of probability density functions well known to statisticians, and in fact the relationship to the lognormal distribution has been explored by Ramsay, Wang and Flanagan (1995). The standard deviation of force seems to be about 8% of the mean force over most of the range of the data. 2 Covariance and correlation functions The covariance function summarizes the dependence of records across diﬀerent argument values, and is computed for all t1 and t2 by N −1 covX (t1 , t2 ) = (N − 1) {xi (t1 ) − x ¯(t1 )}{xi (t2 ) − x ¯(t2 )}.

2 Samples of functional data In general, we are concerned with a collection or sample of functional data, rather than just a single function x. Speciﬁcally, the record or observation of the function xi might consist of ni pairs (tij , yij ), j = 1, . . , ni . It may be that the argument values tij are the same for each record, but they may also vary from record to record. It may be that the interval T over which data are collected also varies from record to record. Normally, the construction of the functional observations xi using the discrete data yij takes place separately or independently for each record i.

Force was sampled 500 times per second. 3 Data display Displaying the results of a functional data analysis can be a challenge. 9, we have already seen that diﬀerent displays of data can bring out diﬀerent features of interest, and that the standard plot of x(t) against t is not necessarily the most informative. It is impossible to be prescriptive about the best type of plot for a given set of data or procedure, but we shall give illustrations of various ways of plotting the results. These are intended to stimulate the reader’s imagination rather than to lay down rigid rules.

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