Data analysis using the method of least squares: extracting the most information from experiments ; with 68 tables
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2006
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Auch als Internetausgabe |
| Physical Description: | XIII, 250 S. graph. Darst. |
| ISBN: | 9783540256748 3540256741 |
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Record in the Search Index
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| adam_text | J. WOLBERG
DATA ANALYSIS
USING THE METHOD
OF LEAST SQUARES
EXTRACTING THE MOST INFORMATION FROM EXPERIMENTS
WITH 58 FIGURES AND 68 TABLES
4U SPRINGER
CONTENTS
CHAPTER 1 INTRODUCTION 1
1.1 QUANTITATIVE EXPERIMENTS 1
1.2 DEALING WITH UNCERTAINTY 5
1.3 STATISTICAL DISTRIBUTIONS 6
THE NORMAL DISTRIBUTION 8
THE BINOMIAL DISTRIBUTION 10
THE POISSON DISTRIBUTION 11
THE DISTRIBUTION 13
THE T DISTRIBUTION 15
THE F DISTRIBUTION 16
1.4 PARAMETRIC MODELS 17
1.5 BASIC ASSUMPTIONS 19
1.6 SYSTEMATIC ERRORS 22
1.7 NONPARAMETRIC MODELS 24
1.8 STATISTICAL LEARNING 27
CHAPTER 2 THE METHOD OF LEAST SQUARES 31
2.1 INTRODUCTION 31
2.2 THE OBJECTIVE FUNCTION 34
2.3 DATA WEIGHTING 38
XII CONTENTS
2.4 OBTAINING THE LEAST SQUARES SOLUTION 44
2.5 UNCERTAINTY IN THE MODEL PARAMETERS 50
2.6 UNCERTAINTY IN THE MODEL PREDICTIONS 54
2.7 TREATMENT OF PRIOR ESTIMATES 60
2.8 APPLYING LEAST SQUARES TO CLASSIFICATION PROBLEMS 64
CHAPTER 3 MODEL EVALUATION 73
3.1 INTRODUCTION 73
3.2 GOODNESS-OF-FIT 74
3.3 SELECTING THE BEST MODEL 79
3.4 VARIANCE REDUCTION 85
3.5 LINEAR CORRELATION 88
3.6 OUTLIERS 93
3.7 USING THE MODEL FOR EXTRAPOLATION 96
3.8 OUT-OF-SAMPLE TESTING 99
3.9 ANALYZING THE RESIDUALS 105
CHAPTER 4 CANDIDATE PREDICTORS 115
4.1 INTRODUCTION 115
4.2 USING THE F DISTRIBUTION 116
4.3 NONLINEAR CORRELATION 122
4.4 RANK CORRELATION 131
CHAPTER 5 DESIGNING QUANTITATIVE EXPERIMENTS 137
5.1 INTRODUCTION 137
5.2 THE EXPECTED VALUE OF THE SUM-OF-SQUARES 139
5.3 THE METHOD OF PREDICTION ANALYSIS 140
5.4 A SIMPLE EXAMPLE: A STRAIGHT LINE EXPERIMENT 143
5.5 DESIGNING FOR INTERPOLATION 147
5.6 DESIGN USING COMPUTER SIMULATIONS 150
5.7 DESIGNS FOR SOME CLASSICAL EXPERIMENTS 155
5.8 CHOOSING THE VALUES OF THE INDEPENDENT VARIABLES 162
CONTENTS XIII
5.9 SOME COMMENTS ABOUT ACCURACY 167
CHAPTER 6 SOFTWARE 169
6.1 INTRODUCTION 169
6.2 GENERAL PURPOSE NONLINEAR REGRESSION PROGRAMS 170
6.3 THE NIST STATISTICAL REFERENCE DATASETS 173
6.4 NONLINEAR REGRESSION CONVERGENCE PROBLEMS 178
6.5 LINEAR REGRESSION: A LURKING PITFALL 184
6.6 MULTI-DIMENSIONAL MODELS 191
6.7 SOFTWARE PERFORMANCE 196
6.8 THE REGRESS PROGRAM 198
CHAPTER 7 KERNEL REGRESSION 203
7.1 INTRODUCTION 203
7.2 KERNEL REGRESSION ORDER ZERO 205
7.3 KERNEL REGRESSION ORDER ONE 208
7.4 KERNEL REGRESSION ORDER TWO 212
7.5 NEAREST NEIGHBOR SEARCHING 215
7.6 KERNEL REGRESSION PERFORMANCE STUDIES 223
7.7 A SCIENTIFIC APPLICATION 225
7.8 APPLYING KERNEL REGRESSION TO CLASSIFICATION 232
7.9 GROUP SEPARATION: AN ALTERNATIVE TO CLASSIFICATION 236
APPENDIX A: GENERATING RANDOM NOISE 239
APPENDIX B: APPROXIMATING THE STANDARD NORMAL DISTRIBUTION 243
REFERENCES 245
INDEX 249
|
| adam_txt |
J. WOLBERG
DATA ANALYSIS
USING THE METHOD
OF LEAST SQUARES
EXTRACTING THE MOST INFORMATION FROM EXPERIMENTS
WITH 58 FIGURES AND 68 TABLES
4U SPRINGER
CONTENTS
CHAPTER 1 INTRODUCTION 1
1.1 QUANTITATIVE EXPERIMENTS 1
1.2 DEALING WITH UNCERTAINTY 5
1.3 STATISTICAL DISTRIBUTIONS 6
THE NORMAL DISTRIBUTION 8
THE BINOMIAL DISTRIBUTION 10
THE POISSON DISTRIBUTION 11
THE DISTRIBUTION 13
THE T DISTRIBUTION 15
THE F DISTRIBUTION 16
1.4 PARAMETRIC MODELS 17
1.5 BASIC ASSUMPTIONS 19
1.6 SYSTEMATIC ERRORS 22
1.7 NONPARAMETRIC MODELS 24
1.8 STATISTICAL LEARNING 27
CHAPTER 2 THE METHOD OF LEAST SQUARES 31
2.1 INTRODUCTION 31
2.2 THE OBJECTIVE FUNCTION 34
2.3 DATA WEIGHTING 38
XII CONTENTS
2.4 OBTAINING THE LEAST SQUARES SOLUTION 44
2.5 UNCERTAINTY IN THE MODEL PARAMETERS 50
2.6 UNCERTAINTY IN THE MODEL PREDICTIONS 54
2.7 TREATMENT OF PRIOR ESTIMATES 60
2.8 APPLYING LEAST SQUARES TO CLASSIFICATION PROBLEMS 64
CHAPTER 3 MODEL EVALUATION 73
3.1 INTRODUCTION 73
3.2 GOODNESS-OF-FIT 74
3.3 SELECTING THE BEST MODEL 79
3.4 VARIANCE REDUCTION 85
3.5 LINEAR CORRELATION 88
3.6 OUTLIERS 93
3.7 USING THE MODEL FOR EXTRAPOLATION 96
3.8 OUT-OF-SAMPLE TESTING 99
3.9 ANALYZING THE RESIDUALS 105
CHAPTER 4 CANDIDATE PREDICTORS 115
4.1 INTRODUCTION 115
4.2 USING THE F DISTRIBUTION 116
4.3 NONLINEAR CORRELATION 122
4.4 RANK CORRELATION 131
CHAPTER 5 DESIGNING QUANTITATIVE EXPERIMENTS 137
5.1 INTRODUCTION 137
5.2 THE EXPECTED VALUE OF THE SUM-OF-SQUARES 139
5.3 THE METHOD OF PREDICTION ANALYSIS 140
5.4 A SIMPLE EXAMPLE: A STRAIGHT LINE EXPERIMENT 143
5.5 DESIGNING FOR INTERPOLATION 147
5.6 DESIGN USING COMPUTER SIMULATIONS 150
5.7 DESIGNS FOR SOME CLASSICAL EXPERIMENTS 155
5.8 CHOOSING THE VALUES OF THE INDEPENDENT VARIABLES 162
CONTENTS XIII
5.9 SOME COMMENTS ABOUT ACCURACY 167
CHAPTER 6 SOFTWARE 169
6.1 INTRODUCTION 169
6.2 GENERAL PURPOSE NONLINEAR REGRESSION PROGRAMS 170
6.3 THE NIST STATISTICAL REFERENCE DATASETS 173
6.4 NONLINEAR REGRESSION CONVERGENCE PROBLEMS 178
6.5 LINEAR REGRESSION: A LURKING PITFALL 184
6.6 MULTI-DIMENSIONAL MODELS 191
6.7 SOFTWARE PERFORMANCE 196
6.8 THE REGRESS PROGRAM 198
CHAPTER 7 KERNEL REGRESSION 203
7.1 INTRODUCTION 203
7.2 KERNEL REGRESSION ORDER ZERO 205
7.3 KERNEL REGRESSION ORDER ONE 208
7.4 KERNEL REGRESSION ORDER TWO 212
7.5 NEAREST NEIGHBOR SEARCHING 215
7.6 KERNEL REGRESSION PERFORMANCE STUDIES 223
7.7 A SCIENTIFIC APPLICATION 225
7.8 APPLYING KERNEL REGRESSION TO CLASSIFICATION 232
7.9 GROUP SEPARATION: AN ALTERNATIVE TO CLASSIFICATION 236
APPENDIX A: GENERATING RANDOM NOISE 239
APPENDIX B: APPROXIMATING THE STANDARD NORMAL DISTRIBUTION 243
REFERENCES 245
INDEX 249 |
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| spelling | Wolberg, John Verfasser aut Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables J. Wolberg Berlin ; Heidelberg ; New York Springer 2006 XIII, 250 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Auch als Internetausgabe Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2668716&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wolberg, John Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| subject_GND | (DE-588)4038974-1 |
| title | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables |
| title_auth | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables |
| title_exact_search | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables |
| title_exact_search_txtP | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables |
| title_full | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables J. Wolberg |
| title_fullStr | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables J. Wolberg |
| title_full_unstemmed | Data analysis using the method of least squares extracting the most information from experiments ; with 68 tables J. Wolberg |
| title_short | Data analysis using the method of least squares |
| title_sort | data analysis using the method of least squares extracting the most information from experiments with 68 tables |
| title_sub | extracting the most information from experiments ; with 68 tables |
| topic | Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| topic_facet | Methode der kleinsten Quadrate |
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