Multivariate Density Estimation : Theory, Practice, and Visualization.
David W. Scott, PhD, is Noah Harding Professor in the Department of Statistics at Rice University. The author of over 100 published articles, papers, and book chapters, Dr. Scott is also Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics. He is recipien...
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Full text (MCPHS users only) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken :
Wiley,
2015
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| Edition: | 2nd ed. |
| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- Title Page; Copyright Page; Contents; Preface to Second Edition; Preface to First Edition; Chapter 1 Representation and Geometry of Multivariate Data; 1.1 Introduction; 1.2 Historical Perspective; 1.3 Graphical Display of Multivariate Data Points; 1.3.1 Multivariate Scatter Diagrams; 1.3.2 Chernoff Faces; 1.3.3 Andrews' Curves and Parallel Coordinate Curves; 1.3.4 Limitations; 1.4 Graphical Display of Multivariate Functionals; 1.4.1 Scatterplot Smoothing by Density Function; 1.4.2 Scatterplot Smoothing by Regression Function; 1.4.3 Visualization of Multivariate Functions.
- 1.4.3.1 Visualizing Multivariate Regression Functions1.4.4 Overview of Contouring and Surface Display; 1.5 Geometry of Higher Dimensions; 1.5.1 Polar Coordinates in d Dimensions; 1.5.2 Content of Hypersphere; 1.5.3 Some Interesting Consequences; 1.5.3.1 Sphere Inscribed in Hypercube; 1.5.3.2 Hypervolume of a Thin Shell; 1.5.3.3 Tail Probabilities of Multivariate Normal; 1.5.3.4 Diagonals in Hyperspace; 1.5.3.5 Data Aggregate Around Shell; 1.5.3.6 Nearest Neighbor Distances; Problems; Chapter 2 Nonparametric Estimation Criteria; 2.1 Estimation of the Cumulative Distribution Function.
- 2.2 Direct Nonparametric Estimation of the Density2.3 Error Criteria for Density Estimates; 2.3.1 MISE for Parametric Estimators; 2.3.1.1 Uniform Density Example; 2.3.1.2 General Parametric MISE Method with Gaussian Application; 2.3.2 The L1 Criterion; 2.3.2.1 L1 versus L2; 2.3.2.2 Three Useful Properties of the L1 Criterion; 2.3.3 Data-Based Parametric Estimation Criteria; 2.4 Nonparametric Families of Distributions; 2.4.1 Pearson Family of Distributions; 2.4.2 When Is an Estimator Nonparametric?; Problems; Chapter 3 Histograms: Theory and Practice.
- 3.1 Sturges' Rule for Histogram Bin-Width Selection3.2 The L2 Theory of Univariate Histograms; 3.2.1 Pointwise Mean Squared Error and Consistency; 3.2.2 Global L2 Histogram Error; 3.2.3 Normal Density Reference Rule; 3.2.3.1 Comparison of Bandwidth Rules; 3.2.3.2 Adjustments for Skewness and Kurtosis; 3.2.4 Equivalent Sample Sizes; 3.2.5 Sensitivity of MISE to Bin Width; 3.2.5.1 Asymptotic Case; 3.2.5.2 Large-Sample and Small-Sample Simulations; 3.2.6 Exact MISE versus Asymptotic MISE; 3.2.6.1 Normal Density; 3.2.6.2 Lognormal Density; 3.2.7 Influence of Bin Edge Location on MISE.
- 3.2.7.1 General Case3.2.7.2 Boundary Discontinuities in the Density; 3.2.8 Optimally Adaptive Histogram Meshes; 3.2.8.1 Bounds on MISE Improvement for Adaptive Histograms; 3.2.8.2 Some Optimal Meshes; 3.2.8.3 Null Space of Adaptive Densities; 3.2.8.4 Percentile Meshes or Adaptive Histograms with Equal Bin Counts; 3.2.8.5 Using Adaptive Meshes versus Transformation; 3.2.8.6 Remarks; 3.3 Practical Data-Based Bin Width Rules; 3.3.1 Oversmoothed Bin Widths; 3.3.1.1 Lower Bounds on the Number of Bins; 3.3.1.2 Upper Bounds on Bin Widths; 3.3.2 Biased and Unbiased CV; 3.3.2.1 Biased CV.
