Please use this identifier to cite or link to this item: https://doi.org/10.1137/S0036141002406229
Title: Asymptotic normality of scaling functions
Authors: Chen, L.H.Y. 
Goodman, T.N.T.
Lee, S.L. 
Keywords: Asymptotic normality
Normal approximation
Probability measures
Scaling functions
Uniform B-splines
Issue Date: 2005
Source: Chen, L.H.Y., Goodman, T.N.T., Lee, S.L. (2005). Asymptotic normality of scaling functions. SIAM Journal on Mathematical Analysis 36 (1) : 323-346. ScholarBank@NUS Repository. https://doi.org/10.1137/S0036141002406229
Abstract: The Gaussian function G(x) = 1/√2πe -x2/2, which has been a classical choice for multiscale representation, is the solution of the scaling equation G(x) = ∫ ℝ αG(αx - y)dg(y), x ∈ ℝ, with scale α > 1 and absolutely continuous measure dg(y)= 1/√2π(α 2-1) e -y2/2(α2-1)dy. It is known that the sequence of normalized B-splines (B n), where B n is the solution of the scaling equation φ(x) = Σ j=0 n1/2 n-1( j n)φ(2x - j), x ∈ ℝ, converges uniformly to G. The classical results on normal approximation of binomial distributions and the uniform B-splines are studied in the broader context of normal approximation of probability measures m n, n = 1, 2,... , and the corresponding solutions φ n of the scaling equations φ n(x) = ∫ ℝ αφ n(αx - y)dm n(y), x ∈ ℝ. Various forms of convergence are considered and orders of convergence obtained. A class of probability densities are constructed that converge to the Gaussian function faster than the uniform B-splines. © 2004 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Mathematical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/102896
ISSN: 00361410
DOI: 10.1137/S0036141002406229
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

6
checked on Feb 15, 2018

WEB OF SCIENCETM
Citations

6
checked on Jan 29, 2018

Page view(s)

24
checked on Feb 12, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.