Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE (www.oxfordhandbooks.com). © Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy and Legal Notice).

date: 13 December 2019

Abstract and Keywords

Semi-nonparametric (SNP) models are models where only a part of the model is parameterized, and the nonspecified part is an unknown function that is represented by an infinite series expansion. Therefore, SNP models are, in essence, models with infinitely many parameters. The theoretical foundation of series expansions of functions is Hilbert space theory, in particular the properties of Hilbert spaces of square integrable real functions. In Hilbert spaces of functions, there exist sequences of orthonormal functions such that any function in this space can be represented by a linear combination of these orthonormal functions. Such orthonormal sequences are called complete. The main purpose of this chapter is to show how these orthonormal functions can be constructed and how to construct general series representations of density and distribution functions. Moreover, in order to explain why this can be done, the necessary Hilbert space theory involved will be reviewed as well.

Keywords: semi-nonparametric models, Hilbert space theory, square integrable functions, orthonormal functions, completeness, series expansions, sieve estimation

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.