Approximation of sign-regular kernels

Thomas A. Knox

Journal of Econometrics, 2022, vol. 226, issue 1, 171-191

Abstract: Parameterized integrals, qy=∫Kx,ydPx, are common in economic applications. To optimize a parameterized integral, or to relate one such integral to others, it is helpful to reduce the rank of the kernel K while controlling approximation error. A bound on the uniform approximation error of Kx,y≈∑i=1nfixgiy also bounds the uniform approximation error of qy≈∑i=1ncigiy=∑i=1n∫fixdPxgiy over all y and all signed measures P whose total variation does not exceed a fixed bound (such as probability measures), which may be useful in optimizing q or in relating q to other parameterized integrals. Bounding the mean squared error or the local error in approximating K generally does not bound the uniform approximation error of q. Many economically interesting kernels of parameterized integrals, including expcxy, the Gaussian probability density function, and a wide class of Green’s functions, satisfy a condition known as strict sign-regularity.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407621001949
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:226:y:2022:i:1:p:171-191

DOI: 10.1016/j.jeconom.2021.07.009

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().