## Data Structures for Computational StatisticsSince the beginning of the seventies computer hardware is available to use programmable computers for various tasks. During the nineties the hardware has developed from the big main frames to personal workstations. Nowadays it is not only the hardware which is much more powerful, but workstations can do much more work than a main frame, compared to the seventies. In parallel we find a specialization in the software. Languages like COBOL for business orientated programming or Fortran for scientific computing only marked the beginning. The introduction of personal computers in the eighties gave new impulses for even further development, already at the beginning of the seven ties some special languages like SAS or SPSS were available for statisticians. Now that personal computers have become very popular the number of pro grams start to explode. Today we will find a wide variety of programs for almost any statistical purpose (Koch & Haag 1995). |

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### Contents

Introduction | 1 |

12 The Need of Interactive Environments | 4 |

13 Modern Computer Soft and Hardware | 18 |

Exploratory Statistical Techniques | 25 |

22 Some Stratifications | 28 |

23 Boxplots | 29 |

24 QuantileQuantile Plot | 31 |

25 Histograms Regressograms and Charts | 33 |

46 Requirements for a Tool Doing Exploratory Projection Pursuit | 166 |

Data Structures | 169 |

52 For Data Objects | 173 |

53 For Linking | 181 |

54 Existing Computational Environments | 187 |

Implementation in XploRe | 197 |

62 Selected Commands in XploRe 32 | 210 |

63 Selected Tools in XploRe 32 | 217 |

26 Bivariate Plots | 40 |

27 Scatterplot Matrices | 46 |

28 Three Dimensional Plots | 48 |

29 Higher Dimensional Plots | 52 |

210 Basic Properties for Graphical Windows | 58 |

Some Statistical Applications | 61 |

32 Teachware | 69 |

33 Regression Methods | 72 |

Exploratory Projection Pursuit | 91 |

42 The Basis of Exploratory Projection Pursuit | 102 |

43 Application to the Swiss Banknote Dataset | 145 |

44 Multivariate Exploratory Projection Pursuit | 148 |

45 Discrete Exploratory Projection Pursuit | 162 |

64 Data Structure in XploRe 40 | 233 |

65 Commands and Macros in XploRe 40 | 237 |

Conclusion | 239 |

The Datasets | 241 |

A2 Berlin Housing Data and Berlin Flat Data | 242 |

A3 Swiss Banknote Data | 245 |

Mean Squared Error of the FriedmanTukey Index | 247 |

Density Estimation on Hexagonal Bins | 257 |

Programs | 263 |

D2 Mathematica Program | 266 |

Tables | 269 |

277 | |

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### Common terms and phrases

3D-scatterplot algorithm allows arrays bandwidth based indices Berlin flat data bins binwidth boxplots brush calculate Chernoff faces cluster analysis coefficients COHV colour command compute data structures DataDesk datapart datapoints descriptive statistics dimension display distance eigenvalues epanechnikov example exploratory projection pursuit Figure Friedman-Tukey index gaussian grand tour graphical objects help system histogram index function integer interactive interface kernel density estimate kernel regression linear regression linking macro matrix median menu multidimensional multidimensional scaling multivariate Nadaraya-Watson estimator nonparametric o o o o OOOOOOOO offers oooooooo o o o o operations optimization parallel coordinate picture polynomial possible principal component analysis problem programming language projection vectors quartic random regression function regression methods result rotation S-Plus scatterplot smoothing parameter SPSS squared standard normal statistical software Swiss banknote dataset Table teachware triweight univariate values variables variance wavelet regression XGobi XploRe