Generalized profiling estimation for global and adaptive penalized spline smoothing

We propose the generalized profiling method to estimate the multiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices ar...

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Vydáno v:Computational statistics & data analysis Ročník 53; číslo 7; s. 2550 - 2562
Hlavní autoři: Cao, Jiguo, Ramsay, James O.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 15.05.2009
Elsevier
Edice:Computational Statistics & Data Analysis
Témata:
Exact sciences and technology
General topics
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Parametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
Variance estimation
Optimization method
Estimator robustness
Adaptive estimation
Penalty method
Optimization
Spline
Variance
Spline approximation
Numerical approximation
Smoothing parameter
Regression function
Regression spline
Mathematical programming
Data analysis
Smoothing methods
Covariance analysis
Variance analysis
Multiple regression
Delta method
Statistical regression
Numerical analysis
Statistical computation
Simulation
Smoothing
Curvature
ISSN:0167-9473, 1872-7352
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Popis
Shrnutí:We propose the generalized profiling method to estimate the multiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices are worked out analytically, using the Implicit Function Theorem if necessary, which leads to fast and stable computation. Our main contribution is developing the modified delta method to estimate the variances of the regression functions, which include the uncertainty of the smoothing parameter estimates. We further develop adaptive penalized spline smoothing to estimate spatially heterogeneous regression functions, where the smoothing parameter is a function that changes along with the curvature of regression functions. The simulations and application show that the generalized profiling method leads to good estimates for the regression functions and their variances.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2008.12.004