| | Statistics seminar:``Spline-backfitted kernel smoothing of additive models" by Jing Wang, UIC | |
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Speaker
| | Jing Wang, UIC |
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| | Date | | Nov 19, 2009 |
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| | Time | | 4:00 pm
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| | Location | | (ROOM CHANGE) 122 Illini Hall |
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| | Sponsor | | Department of Statistics |
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| | E-Mail | | office@illinois.edu |
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| | Phone | | 3-2167 |
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| | Event type | | Seminar |
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| | Views | | 420 |
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| Abstract: A great deal of effort has been devoted to the inference of
additive model in the last decade. Among existing procedures, the kernel
type are too costly to implement for high dimensions or large sample
sizes, while the spline type provide no asymptotic distribution or
uniform convergence. We propose a one step backfitting estimator of the
component function in an additive regression model, using spline
estimators in the first stage followed by kernel/local linear
estimators. Under weak conditions, the proposed estimator's pointwise
distribution is asymptotically equivalent to an univariate kernel/local
linear estimator, hence the dimension is effectively reduced to one at
any point. This dimension reduction holds uniformly over an interval
under assumptions of normal errors. Monte Carlo evidence supports the
asymptotic results for dimensions ranging from low to very high, and
sample sizes ranging from moderate to large. The proposed confidence
band is applied to the Boston housing data for linearity diagnosis. |
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