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Activity Number:
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279
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #304792 |
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Title:
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Orthogonal Series Density Estimation Methodology
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Author(s):
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Serge B. Provost*+ and Min Jiang
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Companies:
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The University of Western Ontario and The University of Western Ontario
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Address:
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Dept. of Statistical and Actuarial Sciences, London, ON, N6A5B7, Canada
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Keywords:
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Kernel density estimation ; Orthogonal polynomials ; Moment-based techniques ; Semiparametric densities ; Density approximation ; Least-squares methodologies
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Abstract:
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Density estimates that are expressible as the product of a weight function and a linear combination of orthogonal polynomials are considered. It is shown that such linear combinations can be equivalently determined from a certain weighted least-squares approach or a moment-matching technique. This leads to a representation of the estimates in terms of sample moments from which a kernel representation is derived. Particular attention is paid to density estimates involving classical orthogonal polynomials. It is explained that the requisite sequence of orthogonal polynomials can be readily generated from a given weight function. Additionally, a criterion is provided for determining the number of terms to be included in the polynomial adjustment. Finally, the semiparametric density estimation methodology is applied to two data sets.
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