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CSDA
2007

Smooth functions and local extreme values

11 years 5 months ago
Smooth functions and local extreme values
Given a sample of n observations y1, . . . , yn at time points t1, . . . , tn we consider the problem of specifying a function ˜f such that ˜f • is smooth, • fits the data in the sense that the residuals yi − ˜f(ti) satisfy the multiresolution criterion 1 √ k − j + 1 k i=j yi − ˜f(ti) < 2 log(n)σ 1 ≤ j ≤ k ≤ n, (1) • is as simple as possible so that ˜f exhibits the minimum number of local extreme values. We analyse in particular a fast method which is based on minimising n i=1 (yi − f(ti))2 + n−1 i=1 λi (fi+1 − fi)2 + (ti+1 − ti)2 where the λi are chosen automatically. The new method can also be applied to density estimation. Key words: Nonparametric regression, modality, smoothness, total variation. 1 Research supported in part by Sonderforschungsbereich 475, University of Dortmund. Preprint submitted to Elsevier Science 30 January 2006
A. Kovac
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CSDA
Authors A. Kovac
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