Local regression and likelihood:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1999
|
| Series: | Statistics and computing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 263 - 284 |
| Physical Description: | XIII, 290 S. graph. Darst. |
| ISBN: | 0387987754 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CLIVE LOADER
LOCAL REGRESSION
AND LIKELIHOOD
WITH 68 FIGURES
SPRINGER
IMAGE 2
CONTENTS
PREFACE V
1 THE ORIGINS OF LOCAL REGRESSION 1
1.1 THE PROBLEM OF GRADUATION 1
1.1.1 GRADUATION USING SUMMATION FORMULAE 2
1.1.2 THE BIAS-VARIANCE TRADE-OFF 7
1.2 LOCAL POLYNOMIAL FITTING 7
1.2.1 OPTIMAL WEIGHTS 8
1.3 SMOOTHING OF TIME SERIES 10
1.4 MODERN LOCAL REGRESSION 11
1.5 EXERCISES 12
2 LOCAL REGRESSION METHODS 15
2.1 THE LOCAL REGRESSION ESTIMATE 15
2.1.1 INTERPRETING THE LOCAL REGRESSION ESTIMATE 18
2.1.2 MULTIVARIATE LOCAL REGRESSION 19
2.2 THE COMPONENTS OF LOCAL REGRESSION 20
2.2.1 BANDWIDTH 20
2.2.2 LOCAL POLYNOMIAL DEGREE 22
2.2.3 THE WEIGHT FUNCTION 23
2.2.4 THE FITTING CRITERION 24
2.3 DIAGNOSTICS AND GOODNESS OF FIT 24
2.3.1 RESIDUAIS 25
2.3.2 INFLUENCE, VARIANCE AND DEGREES OF FREEDOM 27
IMAGE 3
X CONTENTS
2.3.3 CONFIDENCE INTERVALS 29
2.4 MODEL COMPARISON AND SELECTION 30
2.4.1 PREDICTION AND CROSS VALIDATION 30
2.4.2 ESTIMATION ERROR AND CP 31
2.4.3 CROSS VALIDATION PLOTS 32
2.5 LINEAR ESTIMATION 33
2.5.1 INFLUENCE, VARIANCE AND DEGREES OF FREEDOM 35
2.5.2 BIAS 37
2.6 ASYMPTOTIC APPROXIMATIONS 38
2.7 EXERCISES 42
3 FITTING WITH LOCFIT 45
3.1 LOCAL REGRESSION WITH LOCFIT 45
3.2 CUSTOMIZING THE LOCAL FIT 47
3.3 THE COMPUTATIONAL MODEL 48
3.4 DIAGNOSTICS 49
3.4.1 RESIDUAIS 49
3.4.2 CROSS VALIDATION 49
3.5 MULTIVARIATE FITTING AND VISUALIZATION 51
3.5.1 ADDITIVE MODELS 53
3.5.2 CONDITIONALLY PARAMETRIC MODELS 55
3.6 EXERCISES 57
4 LOCAL LIKELIHOOD ESTIMATION 59
4.1 THE LOCAL LIKELIHOOD MODEL 59
4.2 LOCAL LIKELIHOOD WITH LOCFIT 62
4.3 DIAGNOSTICS FOR LOCAL LIKELIHOOD 66
4.3.1 DEVIANCE 66
4.3.2 RESIDUAIS FOR LOCAL LIKELIHOOD 67
4.3.3 CROSS VALIDATION AND AIC 68
4.3.4 OVERDISPERSION 70
4.4 THEORY FOR LOCAL LIKELIHOOD ESTIMATION 72
4.4.1 WHY MAXIMIZE THE LOCAL LIKELIHOOD? 72
4.4.2 LOCAL LIKELIHOOD EQUATIONS 72
4.4.3 BIAS, VARIANCE AND INFLUENCE 74
4.5 EXERCISES 76
5 DENSITY ESTIMATION 79
5.1 LOCAL LIKELIHOOD DENSITY ESTIMATION 79
5.1.1 HIGHER ORDER KERNELS 81
5.1.2 POISSON PROCESS RATE ESTIMATION 82
5.1.3 DISCRETE DATA 82
5.2 DENSITY ESTIMATION IN LOCFIT 83
5.2.1 MULTIVARIATE DENSITY EXAMPLES 86
5.3 DIAGNOSTICS FOR DENSITY ESTIMATION 87
IMAGE 4
CONTENTS XI
5.3.1 RESIDUAIS FOR DENSITY ESTIMATION 88
5.3.2 INFLUENCE, CROSS VALIDATION AND AIC 90
5.3.3 SQUARED ERROR METHODS 92
5.3.4 IMPLEMENTATION 93
5.4 SOME THEORY FOR DENSITY ESTIMATION 95
5.4.1 MOTIVATION FOR THE LIKELIHOOD 95
5.4.2 EXISTENCE AND UNIQUENESS 96
5.4.3 ASYMPTOTIC REPRESENTATION 97
5.5 EXERCISES 98
6 FLEXIBLE LOCAL REGRESSION 101
6.1 DERIVATIVE ESTIMATION 101
6.1.1 IDENTINABILITY AND DERIVATIVE ESTIMATION 102
6.1.2 LOCAL SLOPE ESTIMATION IN LOCFIT 104
6.2 ANGULAR AND PERIODIC DATA 105
6.3 ONE-SIDED SMOOTHING 110
6.4 ROBUST SMOOTHING 113
6.4.1 CHOICE OF ROBUSTNESS CRITERION 114
6.4.2 CHOICE OF SCALE ESTIMATE 115
6.4.3 LOCFIT IMPLEMENTATION 115
6.5 EXERCISES 116
7 SURVIVAL AND FAILURE TIME ANALYSIS 119
7.1 HAZARD RATE ESTIMATION 120
7.1.1 CENSORED SURVIVAL DATA 120
7.1.2 THE LOCAL LIKELIHOOD MODEL 121
7.1.3 HAZARD RATE ESTIMATION IN LOCFIT 122
7.1.4 COVARIATES 123
7.2 CENSORED REGRESSION 124
7.2.1 TRANSFORMATIONS AND ESTIMATES 126
7.2.2 NONPARAMETRIC TRANSFORMATIONS 127
7.3 CENSORED LOCAL LIKELIHOOD 129
7.3.1 CENSORED LOCAL LIKELIHOOD IN LOCFIT 130
7.4 EXERCISES 135
8 DISCRIMINATION AND CLASSIFICATION 138
8.1 DISCRIMINANT ANALYSIS 139
8.2 CLASSIFICATION WITH LOCFIT 140
8.2.1 LOGISTIC REGRESSION 140
8.2.2 DENSITY ESTIMATION 142
8.3 MODEL SELECTION FOR CLASSIFICATION 144
8.4 MULTIPLE CLASSES 147
8.5 MORE ON MISCLASSIFICATION RATES 151
8.5.1 POINTWISE MISCLASSIFICATION 152
8.5.2 GLOBAL MISCLASSIFICATION 153
IMAGE 5
XII CONTENTS
8.6 EXERCISES 155
9 VARIANCE ESTIMATION AND GOODNESS OF FIT 157
9.1 VARIANCE ESTIMATION 157
9.1.1 OTHER VARIANCE ESTIMATES 159
9.1.2 NONHOMOGENEOUS VARIANCE 160
9.1.3 GOODNESS OF FIT TESTING 163
9.2 INTERVAL ESTIMATION 165
9.2.1 POINTWISE CONFIDENCE INTERVALS 165
9.2.2 SIMULTANEOUS CONFIDENCE BANDS 166
9.2.3 LIKELIHOOD MODELS 169
9.2.4 MAXIMAL DEVIATION TESTS 170
9.3 EXERCISES 172
10 BANDWIDTH SELECTION 174
10.1 APPROACHES TO BANDWIDTH SELECTION 175
10.1.1 CLASSICAL APPROACHES 175
10.1.2 PLUG-IN APPROACHES 176
10.2 APPLICATION OF THE BANDWIDTH SELECTORS 179
10.2.1 OLD FAITHFUL 180
10.2.2 THE CLAW DENSITY 183
10.2.3 AUSTRALIAN INSTITUTE OF SPORT DATASET 186
10.3 CONCLUSIONS AND FURTHER READING 188
10.4 EXERCISES 190
11 ADAPTIVE PARAMETER CHOICE 192
11.1 LOCAL GOODNESS OF FIT 193
11.1.1 LOCAL CP 193
11.1.2 LOCAL CROSS VALIDATION 195
11.1.3 INTERSECTION OF CONFIDENCE INTERVALS 196
11.1.4 LOCAL LIKELIHOOD 196
11.2 FITTING LOCALLY ADAPTIVE MODELS 197
11.3 EXERCISES 205
12 COMPUTATIONAL METHODS 206
12.1 LOCAL FITTING AT A POINT 206
12.2 EVALUATION STRUCTURES 208
12.2.1 GROWING ADAPTIVE TREES 209
12.2.2 INTERPOLATION METHODS 212
12.2.3 EVALUATION STRUCTURES IN LOCFIT 214
12.3 INFIUENCE AND VARIANCE FUNCTIONS 215
12.4 DENSITY ESTIMATION 216
12.5 EXERCISES 217
IMAGE 6
CONTENTS XIII
13 OPTIMIZING LOCAL REGRESSION 220
13.1 OPTIMAL RATES OF CONVERGENCE 220
13.2 OPTIMAL CONSTANTS 224
13.3 MINIMAX LOCAL REGRESSION 227
13.3.1 IMPLEMENTATION 229
13.4 DESIGN ADAPTATION AND MODEL INDEXING 231
13.5 EXERCISES 233
A INSTALLING LOCFIT IN R, S AND S-PLUS 235
A.L INSTALLATION, S-PLUS FOR WINDOWS 235
A.2 INSTALLATION, S-PLUS 3, UNIX 236
A.3 INSTALLATION, S-PLUS 5.0 237
A.4 INSTALLING IN R 238
B ADDITIONAL FEATURES: LOCFIT IN S 239
B.L PREDICTION 239
B.2 CALLING L O C F I TO 240
B.2.1 EXTRACTING FROM A FIT 240
B.2.2 ITERATIVE USE OF L O C F IT () 241
B.3 ARITHMETIC OPERATORS AND MATH FUNCTIONS 243
B.4 TRELLIS TRICKS 244
C C-LOCFIT 246
C.L INSTALLATION 246
C.L.L WINDOWS 95, 98 AND NT 246
C.1.2 UNIX . . 246
C.2 USING C-LOCFIT 247
C.2.1 DATA IN C-LOCFIT 248
C.3 FITTING WITH C-LOCFIT 250
C.4 PREDICTION 251
C.5 SOME ADDITIONAL COMMANDS 251
D PLOTS FROM C-LOCFIT 252
D.L THE PLOTDATA COMMAND 253
D.2 THE P L O T F IT COMMAND 253
D.3 OTHER PLOT OPTIONS 256
REFERENCES 257
INDEX 279
|
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| dewey-search | 519.5/36 519.5/36 21 |
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| indexdate | 2024-07-09T18:33:46Z |
| institution | BVB |
| isbn | 0387987754 |
| language | German |
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| physical | XIII, 290 S. graph. Darst. |
| publishDate | 1999 |
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| series2 | Statistics and computing |
| spelling | Loader, Clive Verfasser aut Local regression and likelihood Clive Loader New York [u.a.] Springer 1999 XIII, 290 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Literaturverz. S. 263 - 284 Analyse de régression Estimation, Théorie de l' Regressieanalyse gtt Schattingstheorie gtt Regression analysis Estimation theory Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Maximum-Likelihood-Schätzung (DE-588)4194624-8 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008701217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Loader, Clive Local regression and likelihood Analyse de régression Estimation, Théorie de l' Regressieanalyse gtt Schattingstheorie gtt Regression analysis Estimation theory Regressionsanalyse (DE-588)4129903-6 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4194624-8 |
| title | Local regression and likelihood |
| title_auth | Local regression and likelihood |
| title_exact_search | Local regression and likelihood |
| title_full | Local regression and likelihood Clive Loader |
| title_fullStr | Local regression and likelihood Clive Loader |
| title_full_unstemmed | Local regression and likelihood Clive Loader |
| title_short | Local regression and likelihood |
| title_sort | local regression and likelihood |
| topic | Analyse de régression Estimation, Théorie de l' Regressieanalyse gtt Schattingstheorie gtt Regression analysis Estimation theory Regressionsanalyse (DE-588)4129903-6 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| topic_facet | Analyse de régression Estimation, Théorie de l' Regressieanalyse Schattingstheorie Regression analysis Estimation theory Regressionsanalyse Maximum-Likelihood-Schätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008701217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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