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Abstract:

In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study whether this assumption holds before making other inferences. In this paper, we develop a test for comparing covariance operators of several functional data samples. The proposed test is based on the Hilbert–Schmidt norm of the difference between estimated covariance operators. In particular, when dealing with two populations, the test statistic is just the squared norm of the difference between the two covariance operators estimators. The asymptotic behaviour of the test statistic under both the null hypothesis and local alternatives is obtained. The computation of the quantiles of the null asymptotic distribution is not feasible in practice. To overcome this problem, a bootstrap procedure is considered. The performance of the test statistic for small sample sizes is illustrated through a Monte Carlo study and on a real data set. © 2017, The Institute of Statistical Mathematics, Tokyo.

Registro:

Documento: Artículo
Título:Testing equality between several populations covariance operators
Autor:Boente, G.; Rodriguez, D.; Sued, M.
Filiación:Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires, 1428, Argentina
Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires, 1428, Argentina
Palabras clave:Asymptotic distribution; Bootstrap calibration; Covariance operators; Functional data analysis; Local alternatives; Asymptotic analysis; Population statistics; Asymptotic behaviour; Asymptotic distributions; Covariance operators; Functional data analysis; Functional datas; Local alternatives; Small Sample Size; Test statistics; Statistical tests
Año:2018
Volumen:70
Número:4
Página de inicio:919
Página de fin:950
DOI: http://dx.doi.org/10.1007/s10463-017-0613-1
Título revista:Annals of the Institute of Statistical Mathematics
Título revista abreviado:Annal. Inst. Stat. Math.
ISSN:00203157
CODEN:AISXA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00203157_v70_n4_p919_Boente

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Citas:

---------- APA ----------
Boente, G., Rodriguez, D. & Sued, M. (2018) . Testing equality between several populations covariance operators. Annals of the Institute of Statistical Mathematics, 70(4), 919-950.
http://dx.doi.org/10.1007/s10463-017-0613-1
---------- CHICAGO ----------
Boente, G., Rodriguez, D., Sued, M. "Testing equality between several populations covariance operators" . Annals of the Institute of Statistical Mathematics 70, no. 4 (2018) : 919-950.
http://dx.doi.org/10.1007/s10463-017-0613-1
---------- MLA ----------
Boente, G., Rodriguez, D., Sued, M. "Testing equality between several populations covariance operators" . Annals of the Institute of Statistical Mathematics, vol. 70, no. 4, 2018, pp. 919-950.
http://dx.doi.org/10.1007/s10463-017-0613-1
---------- VANCOUVER ----------
Boente, G., Rodriguez, D., Sued, M. Testing equality between several populations covariance operators. Annal. Inst. Stat. Math. 2018;70(4):919-950.
http://dx.doi.org/10.1007/s10463-017-0613-1