Nonparametric curve estimation: methods, theory, and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 411 S. Illustrationen |
| ISBN: | 0387987401 |
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Record in the Search Index
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Contents
Preface vii
1 Introduction 1
1.1 Density Estimation in the Exploration and Presentation
of Data 1
1.2 Nonparametric Regression 10
1.3 Time Series Analysis 12
2 Orthonormal Series and Approximation 17
2.1 Introduction to Series Approximation 17
2.2 How Fast Fourier Coefficients May Decrease 30
2.3 Special Topic: Geometry of Square Integrable Functions . 34
2.4 Special Topic: Classical Trigonometric Series 39
2.5 Special Topic: Wavelets 47
2.6 Special Topic: More Orthonormal Systems 51
2.7 Exercises 55
2.8 Notes 57
3 Density Estimation for Small Samples 59
3.1 Universal Orthogonal Series Estimator 59
3.2 Lower Bounds (Oracle Inequalities) 72
3.3 Data Driven Estimators 77
3.4 Case Study: Survival Analysis 79
3.5 Case Study: Data Contaminated by Measurement Errors . 85
3.6 Case Study: Length Biased Data 91
xii Contents
3.7 Case Study: Incorporating Special Features 95
3.8 Special Topic: Goodness of Fit Tests 98
3.9 Special Topic: Basis Selection 105
3.10 Practical Seminar 108
3.11 Exercises 112
3.12 Notes 116
4 Nonparametric Regression for Small Samples 118
4.1 Classical Model of Homoscedastic Nonparametric
Regression 119
4.2 Heteroscedastic Nonparametric Regression 126
4.3 Estimation of Scale Function 131
4.4 Wavelet Estimator for Spatially Inhomogeneous
Functions 134
4.5 Case Study: Binary and Poisson Regressions 141
4.6 Case Study: Quantile and Robust Regression 145
4.7 Case Study: Mixtures Regression 151
4.8 Case Study: Dependent Errors 153
4.9 Case Study: Ordered Categorical Data 158
4.10 Case Study: Learning Machine for Inverse Problems with
Unknown Operator 161
4.11 Case Study: Measurement Errors in Predictors 165
4.12 Practical Seminar 168
4.13 Exercises 172
4.14 Notes i 179
5 Nonparametric Time Series Analysis for Small Samples 181
5.1 Estimation of Trend and Seasonal Components and Scale
Function 181
5.2 Estimation of Spectral Density 188
5.3 Example of the Nonparametric Analysis of a Time Series . 194
5.4 Case Study: Missing Observations 201
5.5 Case Study: Hidden Components 203
5.6 Case Study: Bivariate Time Series 210
5.7 Case Study: Dynamic Model and Forecasting 215
5.8 Case Study: Change Point Problem 218
5.9 Practical Seminar 221
5.10 Exercises 224
5.11 Notes 228
6 Estimation of Multivariate Functions for Small Samples 230
6.1 Series Approximation of Multivariate Functions 231
6.2 Density Estimation 235
6.3 Density Estimation in Action: Discriminant Analysis . . . 239
6.4 Nonparametric Regression 242
Contents xiii
6.5 Additive Regression Model 245
6.6 Case Study: Conditional Density 249
6.7 Practical Seminar 253
6.8 Exercises 254
6.9 Notes 258
7 Filtering and Asymptotics 259
7.1 Recovery of a Signal Passed Through Parallel Gaussian
Channels 259
7.2 Filtering a Signal from White Noise 271
7.3 Rate Optimal Estimation When Smoothness Is Known . . 277
7.4 Adaptive Estimation 281
7.5 Multivariate Functions 301
7.6 Special Topic: Estimation of Quadratic Functionals . 304
7.7 Special Topic: Racing for Constants 308
7.8 Special Topic: Confidence Intervals, Confidence Bands,
and Hypothesis Testing 311
7.9 Exercises 314
7.10 Notes 319
8 Nonseries Methods 323
8.1 The Histogram 323
8.2 The Naive Density Estimator 324
8.3 Kernel Estimator 325
8.4 Local Polynomial Regression 334
8.5 The Nearest Neighbor Method 338
8.6 The Maximum Likelihood Method 340
8.7 Spline Approximation 343
8.8 Neural Networks 349
8.9 Asymptotic Analysis of Kernel Estimates 352
8.10 Data Driven Choice of Smoothing Parameters 358
8.11 Practical Seminar 360
8.12 Exercises 362
8.13 Notes 366
Appendix A Fundamentals of Probability and Statistics 367
Appendix B Software 391
References 394
Author Index 403
Subject Index 407 |
| any_adam_object | 1 |
| author | Efromovich, Sam |
| author_GND | (DE-588)12139946X |
| author_facet | Efromovich, Sam |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV012682880 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA278.8.E35 1999 |
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| dewey-full | 519.521 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 21 519.5 |
| dewey-search | 519.5 21 519.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-09-20T04:28:38Z |
| institution | BVB |
| isbn | 0387987401 |
| language | English |
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| spelling | Efromovich, Sam Verfasser (DE-588)12139946X aut Nonparametric curve estimation methods, theory, and applications Sam Efromovich New York [u.a.] Springer 1999 XIII, 411 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Curve fitting gtt Dichtheid gtt Estimation, Théorie de l' Estimation, Théorie de l' ram Filtering (signalen) gtt Non-parametrische statistiek gtt Regressieanalyse gtt Schattingstheorie gtt Stastistique non-paramétrique ram Statistique non-paramétrique Tijdreeksen gtt Nonparametric statistics Estimation theory Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Glatte Kurve (DE-588)4157470-9 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Schätzung (DE-588)4193791-0 s Glatte Kurve (DE-588)4157470-9 s DE-604 Nichtparametrische Statistik (DE-588)4226777-8 s Nichtparametrische Schätzung (DE-588)4203980-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008620073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Efromovich, Sam Nonparametric curve estimation methods, theory, and applications Curve fitting gtt Dichtheid gtt Estimation, Théorie de l' Estimation, Théorie de l' ram Filtering (signalen) gtt Non-parametrische statistiek gtt Regressieanalyse gtt Schattingstheorie gtt Stastistique non-paramétrique ram Statistique non-paramétrique Tijdreeksen gtt Nonparametric statistics Estimation theory Nichtparametrische Schätzung (DE-588)4203980-0 gnd Schätzung (DE-588)4193791-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Glatte Kurve (DE-588)4157470-9 gnd |
| subject_GND | (DE-588)4203980-0 (DE-588)4193791-0 (DE-588)4129903-6 (DE-588)4226777-8 (DE-588)4157470-9 |
| title | Nonparametric curve estimation methods, theory, and applications |
| title_auth | Nonparametric curve estimation methods, theory, and applications |
| title_exact_search | Nonparametric curve estimation methods, theory, and applications |
| title_full | Nonparametric curve estimation methods, theory, and applications Sam Efromovich |
| title_fullStr | Nonparametric curve estimation methods, theory, and applications Sam Efromovich |
| title_full_unstemmed | Nonparametric curve estimation methods, theory, and applications Sam Efromovich |
| title_short | Nonparametric curve estimation |
| title_sort | nonparametric curve estimation methods theory and applications |
| title_sub | methods, theory, and applications |
| topic | Curve fitting gtt Dichtheid gtt Estimation, Théorie de l' Estimation, Théorie de l' ram Filtering (signalen) gtt Non-parametrische statistiek gtt Regressieanalyse gtt Schattingstheorie gtt Stastistique non-paramétrique ram Statistique non-paramétrique Tijdreeksen gtt Nonparametric statistics Estimation theory Nichtparametrische Schätzung (DE-588)4203980-0 gnd Schätzung (DE-588)4193791-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Glatte Kurve (DE-588)4157470-9 gnd |
| topic_facet | Curve fitting Dichtheid Estimation, Théorie de l' Filtering (signalen) Non-parametrische statistiek Regressieanalyse Schattingstheorie Stastistique non-paramétrique Statistique non-paramétrique Tijdreeksen Nonparametric statistics Estimation theory Nichtparametrische Schätzung Schätzung Regressionsanalyse Nichtparametrische Statistik Glatte Kurve |
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