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Activity Number:
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422
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #300746 |
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Title:
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Applications of Orthonormal Bases to Nonparametric Inference
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Author(s):
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Boris Iglewicz*+ and Inna Chervoneva
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Companies:
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Temple University and Thomas Jefferson University
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Address:
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1810 N 13th St., Philadelphia, PA, 19122-6012,
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Keywords:
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clustered data ; density representation ; Fourier coefficients ; Kolmogorov-Smirnov ; non-Gaussian ; orthogonal series
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Abstract:
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The Kolmogorov-Smirnov test and its multisample generalizations are the classic examples of nonparametric tests for detecting general distributional differences between two or more independent samples. In this work we develop an alternative nonparametric methodology for detecting general differences among continuous distributions using orthonormal bases. We propose representing a density function with a finite vector of its estimated Fourier coefficients with respect to some orthonormal basis and modeling those Fourier coefficients as functions of fixed and possibly random effects. We establish asymptotic normality of the estimated Fourier coefficients vector for a wide class of orthonormal bases and propose an unbiased and consistent estimator of its asymptotic covariance matrix. Our approach allows simultaneous detection of differences attributable to various factors, but requires a sufficiently large number of observations per each cluster with the same fixed and random effects realizations. This work was motivated by actual multi-level clustered non-Gaussian datasets from genetic studies.
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