## Adaptive Bayesian Regression Splines in Semiparametric Generalized Linear Models (1998)

Venue: | Journal of Computational and Graphical Statistics |

Citations: | 22 - 2 self |

### BibTeX

@ARTICLE{Biller98adaptivebayesian,

author = {Clemens Biller},

title = {Adaptive Bayesian Regression Splines in Semiparametric Generalized Linear Models},

journal = {Journal of Computational and Graphical Statistics},

year = {1998},

volume = {9},

pages = {122--140}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents a fully Bayesian approach to regression splines with automatic knot selection in generalized semiparametric models for fundamentally non--Gaussian responses. In a basis function representation of the regression spline we use a B--spline basis. The reversible jump Markov chain Monte Carlo method allows for simultaneous estimation both of the number of knots and the knot placement, together with the unknown basis coefficients determining the shape of the spline. Since the spline can be represented as design matrix times unknown (basis) coefficients, it is straightforward to include additionally a vector of covariates with fixed effects, yielding a semiparametric model. The method is illustrated with data sets from the literature for curve estimation in generalized linear models, the Tokyo rainfall data and the coal mining disaster data, and by a credit--scoring problem for generalized semiparametric models. Keywords: B--spline basis; knot selection; nonnormal response...

### Citations

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(Show Context)
Citation Context ...., in Schumaker (1993) or Lyche and Str��m (1996). Further, due to the Bayesian approach using Markov chain Monte Carlo methods, extensions of the semiparametric model to generalized additive mode=-=ls (Hastie and Tibshirani, 1990-=-) or the more general varying--coefficient models (Hastie and Tibshirani, 1993) are possible without much problems. With regard to Markov chain Monte Carlo methods, other approaches for updating fixed... |

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Citation Context ...ile in the backward steps they delete knots yielding the model being optimal for the generalized crossvalidation score. A Bayesian approach using reversible jump Markov chain Monte Carlo (RJMCMC, see =-=Green, 1995-=-) is presented by Denison, Mallick and Smith (1998). In each iteration they choose the set of knots by RJMCMC methods, and given these knots the spline is estimated by the usual least squares approach... |

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Citation Context ...proach to adaptive regression splines with three examples. The first two are data from the literature for curve estimation with discrete response, the Tokyo rainfall data (see e.g. Kitagawa, 1987, or =-=Fahrmeir and Tutz, 1997-=-) and the coal mining disaster data (see e.g. Eilers and Marx, 1996). The third example is an application of the semiparametric model to credit--scoring data described in Fahrmeir and Tutz (1997). 4.1... |

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Citation Context ...Placement of a knot in a certain aera yields more flexibility of f in that aera. Since finding the right number and location of knots by visual inspection of the data is impossible in most cases (see =-=Eubank, 1988-=-, Section 7.2), we need data driven methods for knot placement to get (in some sense) nearly optimal estimators f . For normal response y, such data driven methods exist. Friedman and Silverman (1989)... |

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Citation Context ...two are data from the literature for curve estimation with discrete response, the Tokyo rainfall data (see e.g. Kitagawa, 1987, or Fahrmeir and Tutz, 1997) and the coal mining disaster data (see e.g. =-=Eilers and Marx, 1996-=-). The third example is an application of the semiparametric model to credit--scoring data described in Fahrmeir and Tutz (1997). 4.1 Rainfall data The response is given by the number of occurrences o... |

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Citation Context ...n approach using Markov chain Monte Carlo methods, extensions of the semiparametric model to generalized additive models (Hastie and Tibshirani, 1990) or the more general varying--coefficient models (=-=Hastie and Tibshirani, 1993-=-) are possible without much problems. With regard to Markov chain Monte Carlo methods, other approaches for updating fixed effects in the generalized linear model (Section 3.2) will be considered, sin... |

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Citation Context ...ate the Bayesian approach to adaptive regression splines with three examples. The first two are data from the literature for curve estimation with discrete response, the Tokyo rainfall data (see e.g. =-=Kitagawa, 1987-=-, or Fahrmeir and Tutz, 1997) and the coal mining disaster data (see e.g. Eilers and Marx, 1996). The third example is an application of the semiparametric model to credit--scoring data described in F... |

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Citation Context ...sian approach using Markov chain Monte Carlo methods, extensions of the semiparametric model to generalized additive models (Hastie and Tibshirani, 1990) or the more general varying{coe cient models (=-=Hastie and Tibshirani, 1993-=-) are possible without much problems. With regard to Markov chain Monte Carlo methods, other approaches for updating xed e ects in the generalized linear model (Section 3.2) will be considered, since ... |

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