Nonparametric smoothing and lack of fit tests:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
1997
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 287 S. graph. Darst. |
| ISBN: | 0387949801 |
Staff View
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| 245 | 1 | 0 | |a Nonparametric smoothing and lack of fit tests |c Jeffrey D. Hart |
| 246 | 1 | 3 | |a Nonparametric smoothing and lack-of-fit tests |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. Introduction 1
2. Some Basic Ideas of Smoothing 4
2.1. Introduction 4
2.2. Local Averaging 5
2.3. Kernel Smoothing 6
2.3.1 Fundamentals 6
2.3.2 Variable Bandwidths 14
2.3.3 Transformations of x 16
2.4. Fourier Series Estimators 19
2.5. Dealing with Edge Effects 28
2.5.1 Kernel Smoothers 29
2.5.2 Fourier Series Estimators 32
2.6. Other Smoothing Methods 35
2.6.1 The Duality of Approximation and Estimation 35
2.6.2 Local Polynomials 37
2.6.3 Smoothing Splines 40
2.6.4 Rational Functions 41
2.6.5 Wavelets 44
3. Statistical Properties of Smoothers 50
3.1. Introduction 50
3.2. Mean Squared Error of Gasser Miiller Estimators 51
3.2.1 Mean Squared Error at an Interior Point 51
3.2.2 Mean Squared Error in the Boundary Region 59
3.2.3 Mean Integrated Squared Error 61
3.2.4 Higher Order Kernels 62
3.2.5 Variable Bandwidth Estimators 63
3.2.6 Estimating Derivatives 64
be
x Contents
3.3. MISE of Trigonometric Series Estimators 65
3.3.1 The Simple Truncated Series Estimator 66
3.3.2 Smoothness Adaptability of Simple Series
Estimators 70
3.3.3 The Rogosinski Series Estimator 71
3.4. Asymptotic Distribution Theory 76
3.5. Large Sample Confidence Intervals 78
4. Data Driven Choice of Smoothing Parameters 84
4.1. Introduction 84
4.2. Description of Methods 85
4.2.1 Cross Validation 85
4.2.2 Risk Estimation 86
4.2.3 Plug in Rules 88
4.2.4 The Hall Johnstone Efficient Method 90
4.2.5 One Sided Cross Validation 90
4.2.6 A Data Analysis 92
4.3. Theoretical Properties of Data Driven Smoothers 93
4.3.1 Asymptotics for Cross Validation, Plug In and
Hall Johnstone Methods 94
4.3.2 One Sided Cross Validation 98
4.3.3 Fourier Series Estimators 105
4.4. A Simulation Study 107
4.5. Discussion 113
5. Classical Lack of Fit Tests 117
5.1. Introduction 117
5.2. Likelihood Ratio Tests 119
5.2.1 The General Case 119
5.2.2 Gaussian Errors 121
5.3. Pure Experimental Error and Lack of Fit 122
5.4. Testing the Fit of Linear Models 124
5.4.1 The Reduction Method 124
5.4.2 Unspecified Alternatives 126
5.4.3 Non Gaussian Errors 129
5.5. Nonparametric Lack of Fit Tests 131
5.5.1 The von Neumann Test 132
5.5.2 A Cusum Test 134
5.5.3 Von Neumann and Cusum Tests as Weighted
Sums of Squared Fourier Coefficients 136
5.5.4 Large Sample Power 137
5.6. Neyman Smooth Tests 140
Contents xi
6. Lack of Fit Tests Based on Linear Smoothers 144
6.1. Introduction 144
6.2. Two Basic Approaches 145
6.2.1 Smoothing Residuals 145
6.2.2 Comparing Parametric and Nonparametric Models 147
6.2.3 A Case for Smoothing Residuals 148
6.3. Testing the Fit of a Linear Model 149
6.3.1 Ratios of Quadratic Forms 149
6.3.2 Orthogonal Series 151
6.3.3 Asymptotic Distribution Theory 152
6.4. The Effect of Smoothing Parameter 157
6.4.1 Power 158
6.4.2 The Significance Trace 160
6.5. Historical and Bibliographical Notes 163
7. Testing for Association via Automated Order
Selection 164
7.1. Introduction 164
7.2. Distributional Properties of Sample Fourier Coefficients 166
7.3. The Order Selection Test 168
7.4. Equivalent Forms of the Order Selection Test 174
7.4.1 A Continuous Valued Test Statistic 174
7.4.2 A Graphical Test 175
7.5. Small Sample Null Distribution of Tn 176
7.5.1 Gaussian Errors with Known Variance 177
7.5.2 Gaussian Errors with Unknown Variance 177
7.5.3 Non Gaussian Errors and the Bootstrap 181
7.5.4 A Distribution Free Test 183
7.6. Variations on the Order Selection Theme 185
7.6.1 Data Driven Neyman Smooth Tests 185
7.6.2 .F Ratio with Random Degrees of Freedom 187
7.6.3 Maximum Value of Estimated Risk 188
7.6.4 Test Based on Rogosinski Series Estimate 188
7.6.5 A Bayes Test 189
7.7. Power Properties 195
7.7.1 Consistency 196
7.7.2 Power of Order Selection, Neyman Smooth and
Cusum Tests 197
7.7.3 Local Alternatives 201
7.7.4 A Best Test? 203
7.8. Choosing an Orthogonal Basis 205
7.9. Historical and Bibliographical Notes 206
xii Contents
8. Data Driven Lack of Fit Tests for General Parametric
Models 208
8.1. Introduction 208
8.2. Testing the Fit of Linear Models 208
8.2.1 Basis Functions Orthogonal to Linear Model 209
8.2.2 Basis Functions Not Orthogonal to Linear Model 213
8.2.3 Special Tests for Checking the Fit of a Polynomial 217
8.3. Testing the Fit of a Nonlinear Model 219
8.3.1 Large Sample Distribution of Test Statistics 219
8.3.2 A Bootstrap Test 221
8.4. Power Properties 223
8.4.1 Consistency 223
8.4.2 Comparison of Power for Two Types of Tests 224
9. Extending the Scope of Application 226
9.1. Introduction 226
9.2. Random x a 226
9.3. Multiple Regression 228
9.4. Testing for Additivity 232
9.5. Testing Homoscedasticity 234
9.6. Comparing Curves 236
9.7. Goodness of Fit 238
9.8. Tests for White Noise 240
9.9. Time Series Trend Detection 248
10. Some Examples 253
10.1. Introduction 253
10.2. Babinet Data 253
10.2.1 Testing for Linearity 253
10.2.2 Model Selection 255
10.2.3 Residual Analysis 257
10.3. Comparing Spectra 258
10.4. Testing for Association Among Several Pairs of Variables 261
10.5. Testing for Additivity 263
Appendix 267
A.I. Error in Approximation of Fos(t) 267
A.2. Bounds for the Distribution of Tcusum 268
References 271
Index 281
|
| any_adam_object | 1 |
| author | Hart, Jeffrey D. |
| author_GND | (DE-588)170904695 |
| author_facet | Hart, Jeffrey D. |
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| author_sort | Hart, Jeffrey D. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 519.5 21 |
| dewey-search | 519.5 519.5 21 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| language | English |
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| spelling | Hart, Jeffrey D. Verfasser (DE-588)170904695 aut Nonparametric smoothing and lack of fit tests Jeffrey D. Hart Nonparametric smoothing and lack-of-fit tests New York Springer 1997 XII, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Ajustement, Tests d' (Statistiques) Estatística larpcal Inferência não paramétrica larpcal Lissage (Statistique) Lissage (Statistique) rasuqam Statistique non paramétrique rasuqam Statistique non-paramétrique Test d'ajustement (Statistiques) rasuqam Smoothing (Statistics) Nonparametric statistics Goodness-of-fit tests Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Güte der Anpassung (DE-588)4202143-1 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s Güte der Anpassung (DE-588)4202143-1 s Nichtparametrisches Verfahren (DE-588)4339273-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007791066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hart, Jeffrey D. Nonparametric smoothing and lack of fit tests Ajustement, Tests d' (Statistiques) Estatística larpcal Inferência não paramétrica larpcal Lissage (Statistique) Lissage (Statistique) rasuqam Statistique non paramétrique rasuqam Statistique non-paramétrique Test d'ajustement (Statistiques) rasuqam Smoothing (Statistics) Nonparametric statistics Goodness-of-fit tests Nichtparametrisches Verfahren (DE-588)4339273-8 gnd Regressionsmodell (DE-588)4127980-3 gnd Güte der Anpassung (DE-588)4202143-1 gnd |
| subject_GND | (DE-588)4339273-8 (DE-588)4127980-3 (DE-588)4202143-1 |
| title | Nonparametric smoothing and lack of fit tests |
| title_alt | Nonparametric smoothing and lack-of-fit tests |
| title_auth | Nonparametric smoothing and lack of fit tests |
| title_exact_search | Nonparametric smoothing and lack of fit tests |
| title_full | Nonparametric smoothing and lack of fit tests Jeffrey D. Hart |
| title_fullStr | Nonparametric smoothing and lack of fit tests Jeffrey D. Hart |
| title_full_unstemmed | Nonparametric smoothing and lack of fit tests Jeffrey D. Hart |
| title_short | Nonparametric smoothing and lack of fit tests |
| title_sort | nonparametric smoothing and lack of fit tests |
| topic | Ajustement, Tests d' (Statistiques) Estatística larpcal Inferência não paramétrica larpcal Lissage (Statistique) Lissage (Statistique) rasuqam Statistique non paramétrique rasuqam Statistique non-paramétrique Test d'ajustement (Statistiques) rasuqam Smoothing (Statistics) Nonparametric statistics Goodness-of-fit tests Nichtparametrisches Verfahren (DE-588)4339273-8 gnd Regressionsmodell (DE-588)4127980-3 gnd Güte der Anpassung (DE-588)4202143-1 gnd |
| topic_facet | Ajustement, Tests d' (Statistiques) Estatística Inferência não paramétrica Lissage (Statistique) Statistique non paramétrique Statistique non-paramétrique Test d'ajustement (Statistiques) Smoothing (Statistics) Nonparametric statistics Goodness-of-fit tests Nichtparametrisches Verfahren Regressionsmodell Güte der Anpassung |
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