Density estimation for statistics and data analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
Chapman & Hall/CRC
1998
|
| Ausgabe: | 1. ed., repr. |
| Schriftenreihe: | Monographs on statistics and applied probability
26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | IX, 175 S. graph. Darst. |
| ISBN: | 0412246201 |
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| 100 | 1 | |a Silverman, Bernard W. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804127282817662976 |
|---|---|
| adam_text | Contents
Preface
Page
ix
Introduction
1
1.1
What is density estimation?
1
1.2
Density estimates in the exploration and presentation
of data
2
1.3
Further reading
5
Survey of existing methods
7
2.1
Introduction
7
2.2
Histograms
7
2.3
The naive estimator
11
2.4
The kernel estimator
13
2.5
The nearest neighbour method
19
2.6
The variable kernel method
21
2.7
Orthogonal series estimators
23
2.8
Maximum penalized likelihood estimators
25
2.9
General weight function estimators
26
2.10
Bounded domains and directional data
29
2.11
Discussion and bibliography
32
The kernel method for univariate data
34
3.1
Introduction
34
3.1.1
Notation and conventions
34
3.1.2
Measures of discrepancy
:
mean square error
and mean integrated square error
35
3.2
Elementary finite sample properties
36
3.2.1
Application to kernel estimates
36
3.3
Approximate properties
38
3.3.1
The bias and variance
38
3.3.2
The ideal window width and kernel
40
vi
CONTENTS
3.4
Choosing the smoothing parameter
43
3.4.1
Subjective choice
44
3.4.2
Reference to a standard distribution
45
3.4.3
Least-squares cross-validation
48
3.4.4
Likelihood cross-validation
52
3.4.5
The test graph method
55
3.4.6
Internal estimation of the density roughness
57
3.5
Computational considerations
61
3.6
A possible bias reduction technique
66
3.6.1
Asymptotic arguments
66
3.6.2
Choice of kernel
68
3.6.3
Discussion
69
3.7
Asymptotic properties
70
3.7.1
Consistency results
71
3.7.2
Rates of convergence
72
4.
The kernel method for multivariate data
75
4.1
Introduction
75
4.2
The kernel method in several dimensions
76
4.2.1
Definition of the multivariate kernel density
estimator
76
4.2.2
Multivariate histograms
78
4.2.3
Scatter plots
81
4.3
Choosing the kernel and the window width
84
4.3.1
Sampling properties
85
4.3.2
Choice of window width for a standard
distribution
86
4.3.3
More sophisticated ways of choosing the win¬
dow width
87
4.4
Computational considerations
88
4.4.1
Regular grids: contour diagrams and per¬
spective views
89
4.4.2
Evaluation at irregular points
91
4.5
Difficulties in high-dimensional spaces
91
4.5.1
The importance of the tails in high dimensions
92
4.5.2
Required sample sizes for given accuracy
93
5
Three important methods
95
5.1
Introduction
95
5.2
The nearest neighbour method
96
5.2.1
Definition and properties
96
CONTENTS
vii
5.2.2
Choice of smoothing parameter
98
5.2.3
Computational hints
99
5.3
Adaptive kernel estimates
100
5.3.1
Definition and general properties
101
5.3.2
The method of
Breiman, Meisel
and
Purceii
102
5.3.3
Choice of the sensitivity parameter
103
5.3.4
Automatic choice of the smoothing parameter
105
5.3.5
Some examples
106
5.4
Maximum penalized likelihood estimators
110
5.4.1
Definition and general discussion
110
5.4.2
The approach of Good and Gaskins
П2
5.4.3
The discrete penalized likelihood approach
114
5.4.4
Penalizing the logarithm of the density
115
5.4.5
Penalized likelihood as a unified approach
117
6
Density estimation in action
120
6.1
Nonparametric discriminant analysis
120
6.1.1
Classical approaches
121
6.1.2
The nonparametric approach
122
6.1.3
Operational details
124
6.1.4
Generalizations for discrete and mixed data
126
6.1.5
Discussion and conclusions
129
6.2
Cluster analysis
130
6.2.1
A hierarchical method
131
6.2.2
Moving objects uphill
132
6.2.3
Sequence-based methods
134
6.3
Bump hunting and testing for multimodality
137
6.3.1
Definitions and motivation
137
6.3.2
Two possible approaches based on density
estimation
138
6.3.3
Critical smoothing
139
6.3.4
Discussion and further references
141
6.4
Simulation and the bootstrap
141
6.4.1
Simulating from density estimates
142
6.4.2
The bootstrap and the smoothed bootstrap
144
6.4.3
A smoothed bootstrap test for multimodality
146
6.5
Estimating quantities that depend on the density
147
6.5.1
Hazard rates
147
6.5.2
Funcţionale
of the density
152
6.5.3
Projection pursuit
153
viii CONTENTS
Bibliography
159
Author index
167
Subject index
170
Monographs on Statistics and Applied Probability
26
Density Estimation for Statistics and Data Analysis
Bernard
W
Silverman
Although there has been a surge of interest in density estimation in recent
years, much of the published research has been concerned with purely technical
matters with insufficient emphasis given to the technique s practical value.
Furthermore, the subject has been rather inaccessible to the general statistician.
The account presented in this book places emphasis on topics of
methodological importance, in the hope that this will facilitate broader practical
application of density estimation and also encourage research into relevant
theoretical work. The book also provides an introduction to the subject for
those with general interests in statistics. The important role of density
estimation as a graphical technique is reflected by the inclusion of more than
fifty graphs and figures throughout the text.
Several contexts in which density estimation can be used are discussed,
including the exploration and presentation of data, nonparametric discriminant
analysis, cluster analysis, simulation and the bootstrap, bump hunting,
projection pursuit, and the estimation of hazard rates and other quantities
that depend on the density. This book includes general survey of methods
available for density estimation. The kernel method, both for univariate and
multivariate data, is discussed in detail, with particular emphasis on ways of
deciding how much to smooth and on computational aspects. Attention is also
given to adaptive methods, which smooth to a greater degree in the tails of
the distribution, and to methods based on the idea of penalized likelihood.
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed., repr. |
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| id | DE-604.BV012627330 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:53Z |
| institution | BVB |
| isbn | 0412246201 |
| language | English |
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| spelling | Silverman, Bernard W. Verfasser aut Density estimation for statistics and data analysis B. W. Silverman 1. ed., repr. Boca Raton u.a. Chapman & Hall/CRC 1998 IX, 175 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 26 Estimation theory Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Dichteschätzung (DE-588)4353528-8 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 Schätztheorie (DE-588)4121608-8 s Dichteschätzung (DE-588)4353528-8 s DE-188 Monographs on statistics and applied probability 26 (DE-604)BV002494005 26 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008578176&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008578176&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Silverman, Bernard W. Density estimation for statistics and data analysis Monographs on statistics and applied probability Estimation theory Nichtparametrische Statistik (DE-588)4226777-8 gnd Schätztheorie (DE-588)4121608-8 gnd Dichteschätzung (DE-588)4353528-8 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4121608-8 (DE-588)4353528-8 |
| title | Density estimation for statistics and data analysis |
| title_auth | Density estimation for statistics and data analysis |
| title_exact_search | Density estimation for statistics and data analysis |
| title_full | Density estimation for statistics and data analysis B. W. Silverman |
| title_fullStr | Density estimation for statistics and data analysis B. W. Silverman |
| title_full_unstemmed | Density estimation for statistics and data analysis B. W. Silverman |
| title_short | Density estimation for statistics and data analysis |
| title_sort | density estimation for statistics and data analysis |
| topic | Estimation theory Nichtparametrische Statistik (DE-588)4226777-8 gnd Schätztheorie (DE-588)4121608-8 gnd Dichteschätzung (DE-588)4353528-8 gnd |
| topic_facet | Estimation theory Nichtparametrische Statistik Schätztheorie Dichteschätzung |
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