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Activity Number:
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220
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #305279 |
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Title:
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The ed Method for Nonparametric Density Estimation and Diagnostic Checking
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Author(s):
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Ryan P. Hafen*+ and William S. Cleveland
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Companies:
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Purdue University and Purdue University
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Address:
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3459 Chaucer Dr., Lafayette, IN, 47909,
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Keywords:
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density estimation ; loess ; visualization ; diagnostics ; modeling
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Abstract:
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The ed method of density estimation takes a model building approach with an estimation method that can readily fit many density patterns in data, and that leads to diagnostic visual displays and algorithms for fast computation for practice. Our two-step estimator begins with a very small bandwidth balloon density estimate at each point in the data, which is the inverse of distance to the $k$th nearest neighbor. A $k$ of about 10 typically works well. We take the log and smooth further using the nonparametric regression method loess that fits polynomials locally using local least squares. The log transformation can perform poorly when the density is close to zero, so we add a grid to the data and adjust for it at the end. The two steps of ed let us use the full power of regression diagnostics to search for loess lack of fit and overfitting to the balloon density estimate.
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