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Discrete approximation of integral operators
Author:
Carsten Franz
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2437-2446
MSC (2000):
Primary 62G20, 45C05
Posted:
February 6, 2006
MathSciNet review:
2213718
Full-text PDF Free Access
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Abstract: A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.
References
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-, A family of multivariate two-sample tests. submitted.
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N. Dunford and J. T. Schwartz, Linear operators. Part I. John Wiley and Sons Inc., New York, 1988. MR 1009162 (90g:47001a)
- 4.
C. Franz, ``Asymptotische Eigenschaften einer neuen Klasse von nichtparametrischen Zwei-Stichproben-Tests.'' Doctoral thesis, University of Hannover, 2004.
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V. Koltchinskii and E. Giné, Random matrix approximation of spectra of integral operators. Bernoulli 6 (2000), 113-167. MR 1781185 (2001e:47080)
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G. Neuhaus, Functional limit theorems for U-statistics in the degenerate case. J. Multivariate Anal. 7 (1977), 424-439. MR 0455084 (56:13324)
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F. Stummel, Diskrete Konvergenz linearer Operatoren. I. Math. Ann. 190 (1970), 45-92. MR 0291870 (45:959)
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-, Diskrete Konvergenz linearer Operatoren. II. Math. Z. 120 (1971), 231-264. MR 0291871 (45:960)
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Additional Information
Carsten Franz
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email:
carsten.franz@gmail.com
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08324-9
PII:
S 0002-9939(06)08324-9
Keywords:
Linear operators,
approximation of eigenvalues,
asymptotic null distribution of degenerated U-statistics
Received by editor(s):
March 9, 2005
Posted:
February 6, 2006
Communicated by:
Edward C. Waymire
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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