Open Access
May 2007 Multivariate wavelet-based shape-preserving estimation for dependent observations
Antonio Cosma, Olivier Scaillet, Rainer von Sachs
Bernoulli 13(2): 301-329 (May 2007). DOI: 10.3150/07-BEJ5066


We introduce a new approach to shape-preserving estimation of cumulative distribution functions and probability density functions using the wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. We discuss conditional quantile estimation for financial time series data as an application. Our methodology can be implemented with B-splines. We show by means of Monte Carlo simulations that it performs well in finite samples and for a data-driven choice of the resolution level.


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Antonio Cosma. Olivier Scaillet. Rainer von Sachs. "Multivariate wavelet-based shape-preserving estimation for dependent observations." Bernoulli 13 (2) 301 - 329, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1127.62030
MathSciNet: MR2331253
Digital Object Identifier: 10.3150/07-BEJ5066

Keywords: B-splines , Conditional quantile , Multivariate process , shape preserving wavelet estimation , time series

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
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