## Multivariate Density Estimation: Theory, Practice, and VisualizationWritten to convey an intuitive feeling for both theory and practice, this book illustrates what a powerful tool density estimation can be when used not only with univariate and bivariate data but also in the higher dimensions of trivariate and quadrivariate information. Major concepts are presented in the context of a histogram in order to simplify the treatment of advanced estimators. The text features numerous graphics, problems and solutions, and references to online four-color illustrations. Theoretical statisticians and practicing engineers won't want to miss this. |

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### Contents

CONTENTS ix | 3 |

CONTENTS | 31 |

Theory and Practice | 51 |

5 | 85 |

Frequency Polygons | 100 |

x | 102 |

6 | 137 |

CONTENTS xi | 195 |

The Curse of Dimensionality and Dimension Reduction | 217 |

Nonparametric Regression and Additive Models | 241 |

Other Applications | 267 |

APPENDIX A Computer Graphics in 脫3 | 296 |

CONTENTS xiii | 302 |

267 | 305 |

Notation and Abbreviations | 311 |

334 | |

### Other editions - View all

Multivariate Density Estimation: Theory, Practice, and Visualization David W. Scott Limited preview - 2015 |

Multivariate Density Estimation: Theory, Practice, and Visualization David W. Scott Limited preview - 2015 |

### Common terms and phrases

ˆf(x adaptive algorithm AMISE applied approximation asymptotic bandwidth bias bins bivariate bootstrap bumps Chernoff faces choice clusters computed Consider contour covariance criterion cross-validation CURSE OF DIMENSIONALITY curve data analysis data points data-based dataset density function derivative DIMENSION REDUCTION Epanechnikov Equation example frequency polygon GEOMETRY OF MULTIVARIATE graphical higher order kernels hypersphere integrated squared interval KERNEL DENSITY ESTIMATORS linear matrix mesh Methods minimizer MISE mixture mixture density mode MULTIVARIATE DATA NONPARAMETRIC ESTIMATION NONPARAMETRIC REGRESSION normal data normal density normal kernel optimal bandwidths oversmoothed parallel coordinates parametric estimator plot pointwise polynomial problem Projection Pursuit random REPRESENTATION AND GEOMETRY result sample sizes scatter diagrams scatterplot Scott Second Edition sepal shifted histogram shown in Figure slices smoother smoothing parameter spline squared error Statist structure surface Terrell Theorem Theory transformation trivariate Tukey univariate values variables variance vector visualization width zero-bias