Activity Number:
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333
- Section on Nonparametric Statistics - Student Paper Awards
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #328381
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Presentation
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Title:
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Optimal Estimation in Functional ANOVA Models with Derivatives
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Author(s):
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Xiaowu Dai* and Peter Chien
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Companies:
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University of Wisconsin Madison and University of Wisconsin-Madison
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Keywords:
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Nonparametric regression;
smoothing spline ANOVA;
partial derivative data;
method of regularization;
minimax rate
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Abstract:
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We establish minimax optimal rates of convergence for nonparametric estimation in functional ANOVA models when data from first-order partial derivatives are available. Our results reveal that partial derivatives can improve convergence rates for function estimation with random designs. In particular, for full $d$-interaction models, the optimal rates with first-order partial derivatives on $p$ covariates are identical to those for $(d-p)$-interaction models without partial derivatives. For additive models, the rates by using all first-order partial derivatives are root-$n$ to achieve the "parametric rate". We also investigate the minimax optimal rates for first-order partial derivative estimations when derivative data are available. Those rates coincide with the optimal rate for estimating the first-order derivative of a univariate function.
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Authors who are presenting talks have a * after their name.