Density estimation for statistics and data analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman and Hall
1986
|
| Series: | Monographs on statistics and applied probability
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 175 S. graph. Darst. |
| ISBN: | 0412246201 9780412246203 |
Staff View
MARC
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| 245 | 1 | 0 | |a Density estimation for statistics and data analysis |
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Record in the Search Index
| _version_ | 1804116574771085312 |
|---|---|
| adam_text | Contents
Preface
Page
ix
1
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
2
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
3
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
^
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 multiwiate 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
Regolar
grids: contour diagrams and per¬
spective views
89
4.4.2
Evaluation at irregular points
91
4.5
Difficulties in high-dimensioiial spaces
91
4.5.1
The importance of the tails in high dimensions
92
4.5.2
Required sample sizes for given accuracy
93
5.1
Introduction
95
5.2
The nearest neighbour method
%
5.2.1
Definition and properties
%
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
112
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
Non
parametric 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
Functional of the density
152
6.5.3
Projection pursuit
153
viii CONTENTS
BlbHography
159
Author
imàtx
167
170
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV002121452 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:41Z |
| institution | BVB |
| isbn | 0412246201 9780412246203 |
| language | English |
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| publisher | Chapman and Hall |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Silverman, Bernard W. Verfasser aut Density estimation for statistics and data analysis London [u.a.] Chapman and Hall 1986 IX, 175 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 26 Dichtheid gtt Estimation, Théorie de l' Waarschijnlijkheidstheorie gtt Estimation theory Dichteschätzung (DE-588)4353528-8 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s DE-604 Nichtparametrische Statistik (DE-588)4226777-8 s Dichteschätzung (DE-588)4353528-8 s 1\p DE-604 Monographs on statistics and applied probability 26 (DE-604)BV002494005 26 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001391019&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Silverman, Bernard W. Density estimation for statistics and data analysis Monographs on statistics and applied probability Dichtheid gtt Estimation, Théorie de l' Waarschijnlijkheidstheorie gtt Estimation theory Dichteschätzung (DE-588)4353528-8 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4353528-8 (DE-588)4226777-8 (DE-588)4121608-8 |
| 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 |
| title_fullStr | Density estimation for statistics and data analysis |
| title_full_unstemmed | Density estimation for statistics and data analysis |
| title_short | Density estimation for statistics and data analysis |
| title_sort | density estimation for statistics and data analysis |
| topic | Dichtheid gtt Estimation, Théorie de l' Waarschijnlijkheidstheorie gtt Estimation theory Dichteschätzung (DE-588)4353528-8 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Dichtheid Estimation, Théorie de l' Waarschijnlijkheidstheorie Estimation theory Dichteschätzung Nichtparametrische Statistik Schätztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001391019&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT silvermanbernardw densityestimationforstatisticsanddataanalysis |