Application of a delta-method for random operators to testing equality of two covariance operators

Autor:	Frits H. Ruymgaart, G. Gaines, K. Kaphle
Rok vydání:	2011
Předmět:	Statistics and Probability Mathematical optimization Constant coefficients Microlocal analysis Applied mathematics Asymptotic distribution Spectral theorem Statistics Probability and Uncertainty Covariance Operator theory Operator norm Fourier integral operator Mathematics
Zdroj:	Mathematical Methods of Statistics. 20:232-245
ISSN:	1934-8045 1066-5307
DOI:	10.3103/s1066530711030057
Popis:	In this paper some useful mathematical tools for the analysis of functional data are applied to the problem of testing the equality of two covariance operators. The test to be used is derived from a univariate likelihood ratio test in conjunction with Roy’s union-intersection principle. The asymptotic distribution and asymptotic power against rather general local alternatives are calculated. Perturbation theory of operators, in particular, a delta-method for smooth functions of operators, is exploited to obtain these theoretical results that are corroborated by some simulations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c00e7c2a911082b273e30df50e97e2ca https://doi.org/10.3103/s1066530711030057 Zobrazit plný text záznamu Full text from SpringerLink