Abstract
We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval—those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial estimators are superior in many respects. However, Legendre polynomial series can be more difficult to construct than trigonometric series, and to overcome this difficulty we show how to modify trigonometric series estimators to make them more competitive.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
