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## Projection Pursuit Regression (1981)

Venue: | Journal of the American Statistical Association |

Citations: | 550 - 6 self |

### Citations

1253 |
Robust locally weighted regression and smoothing scatterplots
- Cleveland
- 1979
(Show Context)
Citation Context ... be formally defined (e.g., Si12(z)dz ), I but for the purpose of this discussion an intuitive notion of smoothness will be sufficient. Many procedures for smoothing have been described (Tukey, 1977, =-=Cleveland, 1979-=-, Gasser and Rosenblatt, 1979). They are based on the notion of local averaging: S(zi) = AVE i-k I j 5 itk (Yj) with suitable adjustment for the boundaries. Here "AVE" can denote the-7mean, median or... |

340 | A projection pursuit algorithm for exploratory data analysis,” - Friedman, Tukey - 1974 |

225 |
An automatic method for finding the greatest or least value of a function“,
- Rosenbrock
- 1960
(Show Context)
Citation Context ...uires several passes over the data); - the search usually starts far from the solution; - the search can be restricted to the unit sphere in Rp. For these reasons, we have chosen a Rosenbrock method (=-=Rosenbrock, 1960-=-) modified to search on the unit sphere. The search is started at the best coordinate direction. On any given search, there is no guarantee that the global optimum will be found. If the local optimum ... |

14 |
General estimates of the intrinsic variability of data in nonlinear regression models
- Breiman, Meisel
- 1976
(Show Context)
Citation Context ...es with asymptotes); use of higher-order polynomials is limited by considerations of sample size and computational feasibility. A hierarchy of piecewise constant (Sonquist, 1970) or piecewise linear (=-=Breiman and Meisel, 1976-=-, Friedman, 1979) models leads to recur--4sive partitioning regression. These procedures basically operate as follows: For a particular predictor and a value of this predictor, the predictor space is... |

12 |
Multivariate Model Building: The Validation of a Search Strategy
- Sonquist
- 1970
(Show Context)
Citation Context ...y low-order polynomials (e.g., surfaces with asymptotes); use of higher-order polynomials is limited by considerations of sample size and computational feasibility. A hierarchy of piecewise constant (=-=Sonquist, 1970-=-) or piecewise linear (Breiman and Meisel, 1976, Friedman, 1979) models leads to recur--4sive partitioning regression. These procedures basically operate as follows: For a particular predictor and a ... |

10 | A tree-structured approach to nonparametric multiple regression
- Friedman
- 1979
(Show Context)
Citation Context ...f higher-order polynomials is limited by considerations of sample size and computational feasibility. A hierarchy of piecewise constant (Sonquist, 1970) or piecewise linear (Breiman and Meisel, 1976, =-=Friedman, 1979-=-) models leads to recur--4sive partitioning regression. These procedures basically operate as follows: For a particular predictor and a value of this predictor, the predictor space is split into two ... |

5 |
Nonparametric regression and its applications (with discussion
- Stone
- 1977
(Show Context)
Citation Context ...regression surface at a point z. is the average of the responses of those observations with predictors in a neighborhood of -x0. These techniques can be shown to have desirable asymptotic properties (=-=Stone, 1977-=-). In high dimensional settings, however, they do not perform well for reasonable sample sizes. The reason is the inherent.sparsity of high-dimensional samples. This is illustrated by the following si... |

5 |
Admissible selection of an accurate and parsimonious normal linear regression model
- Stone
- 1981
(Show Context)
Citation Context ...mooth indicates that including this projection into the model would only increase the variance, while not reducing the bias. One can also employ a more formal procedure based on cross validation (see =-=Stone, 1981-=-). The PPR procedure can clearly be applied to the residuals from any initial model. If the initial model does not fit the data well, PPR will so indicate by augmenting it. All stepwise procedures hav... |

4 |
Smoothing Techniques for Curve Estimation
- Gasser, Rosenblatt
- 1979
(Show Context)
Citation Context ...ned (e.g., Si12(z)dz ), I but for the purpose of this discussion an intuitive notion of smoothness will be sufficient. Many procedures for smoothing have been described (Tukey, 1977, Cleveland, 1979, =-=Gasser and Rosenblatt, 1979-=-). They are based on the notion of local averaging: S(zi) = AVE i-k I j 5 itk (Yj) with suitable adjustment for the boundaries. Here "AVE" can denote the-7mean, median or other ways of "averaging". T... |

1 | Van Hove analysis of the reactions n'prr-n'n+p and n+mtntm- at 16 GeV/C - Ballam, Chadwick, et al. - 1971 |