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Testing the Equality of Covariance Operators in Functional Samples
Author(s) -
FREMDT STEFAN,
STEINEBACH JOSEF G.,
HORVÁTH LAJOS,
KOKOSZKA PIOTR
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00796.x
Subject(s) - mathematics , covariance , statistic , asymptotic distribution , parametric statistics , degrees of freedom (physics and chemistry) , test statistic , statistics , chi square test , analysis of covariance , statistical hypothesis testing , dimension (graph theory) , pure mathematics , physics , quantum mechanics , estimator
. We propose a non‐parametric test for the equality of the covariance structures in two functional samples. The test statistic has a chi‐square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension reduction needed to represent the data. Detailed analysis of the asymptotic properties is developed. Finite sample perfo‐rmance is examined by a simulation study and an application to egg‐laying curves of fruit flies.