Read e-book online 150 Masterpieces of Drawing PDF

By Anthony Toney

ISBN-10: 0486316920

ISBN-13: 9780486316925

Full-page reproductions of drawings from the early fifteenth century to the tip of the 18th century, all superbly reproduced: Rembrandt, Michelangelo, Dürer, Fragonard, Urs Graf, Wouwerman, many others. fine shopping ebook, version publication for artists.

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1984), climatology (Ramsay and Silverman, 1997) or linguistics (Marx and Eilers, 1996). •^We would like to thank all the members and participants of the working group on functional data STAPH from Toulouse for helpful discussions. 50 In this context we are faced with the problem of estimating the hnk between a real random response Y and a square integrable random function X defined on some compact set C of R through a sample (X^, F^), i = 1 , . . ,n drawn from {X,Y). Of course, in practice the curves X^'s are discretized (possibly not at the same points) and then statistical multivariate methods may be applied to these random vectors with special attention to the problems of high dimension and multicollinearity inherent to this kind of data.

Let us denote by TT^J , j = 1 , . . ,p, the proportion of land use of crop j in pixel z of 1 km^. In our apphcation the observed area is about 40km x40km so that 2 = 1 , . . , n = 1554. Ten (p = 10) different classes of crops were present. The curves of reflectance for each pixel z, in each channel and index, are denoted by Xi = [Xi{ti)^... ,Xi{tK)] where ti < ... < tk < - - - < t^ are the instants of measure. The images in which the clouds were too important were removed to finally get K = 39 different images from March to August 1998.

Marx and Eilers (1999) use a smooth B-spUne expansion for a and introduce a difference penalty in a log-likelihood criterion in the context of smoothed generalized linear regression. Direct estimation of the functional ^ has been achieved in Cardot et al. (1999) by means of a functional PCR, in the setting of a predictor valued in a general real separable Hilbert space. A smooth version of this Functional Principal Components Regression has been studied in Cardot, Ferraty and Sarda (2003). We define below the spline estimators proposed by Cardot, Ferraty, and Sarda (2003) which combines ideas from Marx and Eilers (1996) and Hastie and Mallows (1993).

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150 Masterpieces of Drawing by Anthony Toney


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