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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Vydáno v:Journal of statistical planning and inference Ročník 141; číslo 1; s. 204 - 219
Hlavní autoři: Ma, Shujie, Yang, Lijian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 2011
Elsevier
Témata:
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
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
ISSN:0378-3758, 1873-1171
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Popis
Shrnutí: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.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.05.028