Spline-backfitted kernel smoothing of partially linear additive model
A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the dat...
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| Published in: | Journal of statistical planning and inference Vol. 141; no. 1; pp. 204 - 219 |
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| Language: | English |
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Elsevier B.V
2011
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| ISSN: | 0378-3758, 1873-1171 |
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| Abstract | A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate and large number of variables confirm the asymptotic results. Application to the Boston housing data serves as a practical illustration of the method. |
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| AbstractList | A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate and large number of variables confirm the asymptotic results. Application to the Boston housing data serves as a practical illustration of the method. |
| Author | Yang, Lijian Ma, Shujie |
| Author_xml | – sequence: 1 givenname: Shujie surname: Ma fullname: Ma, Shujie – sequence: 2 givenname: Lijian surname: Yang fullname: Yang, Lijian email: yang@stt.msu.edu |
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| Keywords | B spline Mixing Bandwidths Nadaraya–Watson estimator Nonparametric regression Local linear estimator Knots Geometric function Bandwith selection Non parametric estimation Data smoothing Additive model Linear model Spline approximation Numerical approximation Estimator efficiency Law of large numbers Mixed distribution Smoothing methods Statistical estimation Statistical decision Kernel method Statistical method Kernels Simulation Nadaraya-Watson estimator |
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| SubjectTerms | Approximations and expansions B spline Bandwidths Exact sciences and technology Functions of a complex variable General topics Knots Local linear estimator Mathematical analysis Mathematics Mixing Nadaraya–Watson estimator Nonparametric regression Numerical analysis Numerical analysis. Scientific computation Numerical approximation Probability and statistics Sciences and techniques of general use Statistics |
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