Interpolation of spatial data: some theory for kriging
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
1999
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008620272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 247 S. graph. Darst. |
| ISBN: | 0387986294 |
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| 100 | 1 | |a Stein, Michael L. |e Verfasser |0 (DE-588)121270564 |4 aut | |
| 245 | 1 | 0 | |a Interpolation of spatial data |b some theory for kriging |c Michael L. Stein |
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| 300 | |a XVII, 247 S. |b graph. Darst. | ||
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|---|---|
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| adam_text | IMAGE 1
MICHAEL L. STEIN
INTERPOLATION OF SPATIAL DATA
SOME THEORY FOR KRIGING
WITH 27 ILLUSTRATIONS
SPRINGER
IMAGE 2
CONTENTS
PREFACE VII
1 LINEAR PREDICTION 1
1.1 INTRODUCTION 1
1.2 BEST LINEAR PREDICTION 2
EXERCISES 3
1.3 HUBERT SPACES AND PREDICTION . 4
EXERCISES 5
1.4 AN EXAMPLE OF A POOR BLP 6
EXERCISES 6
1.5 BEST LINEAR UNBIASED PREDICTION 7
EXERCISES 9
1.6 SOME RECURRING THEMES 10
THE MATERN MODEL 12
BLPS AND BLUPS 12
INFERENCE FOR DIFFERENTIABLE RANDOM NELDS 13
NESTED MODEIS ARE NOT TENABLE 13
1.7 SUMMARY OF PRACTICAL SUGGESTIONS 14
2 PROPERTIES OF RANDOM FIELDS 15
2.1 PRELIMINARIES 15
STATIONARITY 16
ISOTROPY 17
EXERCISE 17
2.2 THE TURNING BANDS METHOD 17
IMAGE 3
XIV CONTENTS
EXERCISE 19
2.3 ELEMENTARY PROPERTIES OF AUTOCOVARIANCE FUNCTIONS . . .. 19
EXERCISE 20
2.4 MEAN SQUARE CONTINUITY AND DIFFERENTIABILITY 20
EXERCISES 22
2.5 SPECTRAL METHODS 22
SPECTRAL REPRESENTATION OF A RANDOM FIELD 23
BOCHNER S THEOREM 24
EXERCISES 25
2.6 TWO CORRESPONDING HUBERT SPACES 26
AN APPLICATION TO MEAN SQUARE DIFFERENTIABILITY 26
EXERCISES 27
2.7 EXAMPLES OF SPECTRAL DENSITIES ON R 27
RATIONAL SPECTRAL DENSITIES 28
PRINCIPAL IRREGULAER TERM 28
GAUSSIAN MODEL 29
TRIANGULAER AUTOCOVARIANCE FUNCTIONS 30
MATERN CLASS 31
EXERCISES 33
2.8 ABELIAN AND TAUBERIAN THEOREMS 33
EXERCISES 35
2.9 RANDOM FIELDS WITH NONINTEGRABLE SPECTRAL DENSITIES . . .. 36
INTRINSIC RANDOM FUNCTIONS 36
SEMIVARIOGRAMS 39
GENERALIZED RANDOM FIELDS 40
EXERCISES 41
2.10 ISOTROPIE AUTOCOVARIANCE FUNCTIONS 42
CHARACTERIZATION 42
LOWER BOUND ON ISOTROPIC AUTOCORRELATION FUNCTIONS . . .. 45
INVERSION FORMULA 46
SMOOTHNESS PROPERTIES 46
MATERN CLASS 48
SPHERICAL MODEL 52
EXERCISES 53
2.11 TENSOR PRODUET AUTOCOVARIANCES 54
EXERCISES 55
3 ASYMPTOTIC PROPERTIES OF LINEAR PREDICTORS 57
3.1 INTRODUCTION 57
3.2 FINITE SAMPLE RESULTS 59
EXERCISE 61
3.3 THE ROLE OF ASYMPTOTICS 61
3.4 BEHAVIOR OF PREDICTION ERRORS IN THE FREQUENCY DOMAIN . . 63
SOME EXAMPLES 63
RELATIONSHIP TO FILTERING THEORY 65
IMAGE 4
CONTENTS XV
EXERCISES 65
3.5 PREDICTION WITH THE WRONG SPECTRAL DENSITY 66
EXAMPLES OF INTERPOLATION 66
AN EXAMPLE WITH A TRIANGULAER AUTOCOVARIANCE FUNCTION . . 67 MORE
CRITICISM OF GAUSSIAN AUTOCOVARIANCE FUNCTIONS . .. 69
EXAMPLES OF EXTRAPOLATION 70
PSEUDO-BLPS WITH SPECTRAL DENSITIES MISSPECIFIED AT HIGH FREQUENCIES 71
EXERCISES 74
3.6 THEORETICAL COMPARISON OF EXTRAPOLATION AND INTERPOLATION 76
AN INTERPOLATION PROBLEM 77
AN EXTRAPOLATION PROBLEM 78
ASYMPTOTICS FOR BLPS 79
INEFFICIENCY OF PSEUDO-BLPS WITH MISSPECIFIED HIGH FREQUENCY BEHAVIOR 81
PRESUMED MSES FOR PSEUDO-BLPS WITH MISSPECIFIED HIGH FREQUENCY BEHAVIOR
85
PSEUDO-BLPS WITH CORRECTLY SPECIFIED HIGH FREQUENCY BEHAVIOR 86
EXERCISES 92
3.7 MEASUREMENT ERRORS 94
SOME ASYMPTOTIC THEORY 95
EXERCISES 97
3.8 OBSERVATIONS ON AN INFINITE LATTICE 97
CHARACTERIZING THE BLP 98
BOUND ON FRACTION OF MSE OF BLP ATTRIBUTABLE TO A SET OF FREQUENCIES 99
ASYMPTOTIC OPTIMALITY OF PSEUDO-BLPS 101
RATES OF CONVERGENCE TO OPTIMALITY 104
PSEUDO-BLPS WITH A MISSPECIFIED MEAN FUNCTION 105
EXERCISES 108
4 EQUIVALENCE OF GAUSSIAN MEASURES AND PREDICTION 109
4.1 INTRODUCTION 109
4.2 EQUIVALENCE AND ORTHOGONALITY OF GAUSSIAN MEASURES . .. 111
CONDITIONS FOR ORTHOGONALITY 111
GAUSSIAN MEASURES ARE EQUIVALENT OR ORTHOGONAL 114
DETERMINING EQUIVALENCE OR ORTHOGONALITY FOR PERIODIC RAN DOM FIELDS 118
DETERMINING EQUIVALENCE OR ORTHOGONALITY FOR NONPERIODIC RANDOM FIELDS
119
MEASUREMENT ERRORS AND EQUIVALENCE AND ORTHOGONALITY . . 122 PROOF OF
THEOREM 1 123
EXERCISES 126
IMAGE 5
XVI CONTENTS
4.3 APPLICATIONS OF EQUIVALENCE OF GAUSSIAN MEASURES TO LINEAR
PREDICTION 129
ASYMPTOTICALLY OPTIMAL PSEUDO-BLPS 130
OBSERVATIONS NOT PART OF A SEQUENCE 132
A THEOREM OF BLACKWELL AND DUBINS 134
WEAKER CONDITIONS FOR ASYMPTOTIC OPTIMALITY OF PSEUDO-BLPS 135
RATES OF CONVERGENCE TO ASYMPTOTIC OPTIMALITY 138
ASYMPTOTIC OPTIMALITY OF BLUPS 138
EXERCISES 139
4.4 JEFFREYS S LAW 140
A BAYESIAN VERSION 141
EXERCISES 143
5 INTEGRATION OF RANDOM FIELDS 144
5.1 INTRODUCTION 144
5.2 ASYMPTOTIC PROPERTIES OF SIMPLE AVERAGE 145
RESULTS FOR SUFFICIENTLY SMOOTH RANDOM FIELDS 147
RESULTS FOR SUFFICIENTLY ROUGH RANDOM FIELDS 148
EXERCISES 149
5.3 OBSERVATIONS ON AN INFINITE LATTICE 150
ASYMPTOTIC MSE OF BLP 150
ASYMPTOTIC OPTIMALITY OF SIMPLE AVERAGE 153
EXERCISES 153
5.4 IMPROVING ON THE SAMPLE MEAN 153
APPROXIMATING / 0 EXP(II/T)DT 153
APPROXIMATING /, Q X , D EXP(IU; T X)DX IN MORE THAN ONE DIMENSION 155
ASYMPTOTIC PROPERTIES OF MODIFIED PREDICTORS 156
ARE CENTERED SYSTEMATIC SAMPLES GOOD DESIGNS? 157
EXERCISES 157
5.5 NUMERICAL RESULTS 157
EXERCISES 159
6 PREDICTING WITH ESTIMATED PARAMETERS 160
6.1 INTRODUCTION 160
6.2 MICROERGODICITY AND EQUIVALENCE AND ORTHOGONALITY OF GAUSSIAN
MEASURES 162
OBSERVATIONS WITH MEASUREMENT ERROR 164
EXERCISES 165
6.3 IS STATISTICAL INFERENCE FOR DIFFERENTIABLE PROCESSES POSSIBLE? 166
AN EXAMPLE WHERE IT IS POSSIBLE 167
EXERCISES 168
IMAGE 6
CONTENTS XVII
6.4 LIKELIHOOD METHODS 169
RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION 170
GAUSSIAN ASSUMPTION 171
COMPUTATIONAL ISSUES 172
SOME ASYMPTOTIC THEORY 174
EXERCISES 175
6.5 MATERN MODEL 176
EXERCISE 178
6.6 A NUMERICAL STUDY OF THE FISHER INFORMATION MATRIX UNDER THE MATERN
MODEL 178
NO MEASUREMENT ERROR AND V UNKNOWN 179
NO MEASUREMENT ERROR AND V KNOWN 181
OBSERVATIONS WITH MEASUREMENT ERROR 182
CONCLUSIONS 186
EXERCISES 188
6.7 MAXIMUM LIKELIHOOD ESTIMATION FOR A PERIODIC VERSION OF THE MATERN
MODEL 188
DISCRETE FOURIER TRANSFORMS 188
PERIODIC CASE 189
ASYMPTOTIC RESULTS 190
EXERCISES 198
6.8 PREDICTING WITH ESTIMATED PARAMETERS 199
JEFFREYS S LAW REVISITED 203
NUMERICAL RESULTS 206
SOME ISSUES REGARDING ASYMPTOTIC OPTIMALITY 210
EXERCISES 211
6.9 AN INSTRUCTIVE EXAMPLE OF PLUG-IN PREDICTION 211
BEHAVIOR OF PLUG-IN PREDICTIONS 214
CROSS-VALIDATION 215
APPLICATION OF MATERN MODEL 218
CONCLUSIONS 220
EXERCISES 223
6.10 BAYESIAN APPROACH 223
APPLICATION TO SIMULATED DATA 225
EXERCISES 226
A MULTIVARIATE NORMAL DISTRIBUTIONS 229
B SYMBOLS 231
REFERENCES 235
INDEX 243
|
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| discipline | Bergbau / Hüttenwesen Mathematik |
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| id | DE-604.BV012683111 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:34:33Z |
| institution | BVB |
| isbn | 0387986294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008620272 |
| oclc_num | 40051990 |
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| owner_facet | DE-824 DE-739 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-521 DE-634 DE-83 DE-11 DE-188 DE-20 |
| physical | XVII, 247 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Stein, Michael L. Interpolation of spatial data some theory for kriging Krigeage Minerais - Echantillonage et estimation ram Stochastische processen gtt Kriging Kriging (DE-588)4339232-5 gnd |
| subject_GND | (DE-588)4339232-5 |
| title | Interpolation of spatial data some theory for kriging |
| title_auth | Interpolation of spatial data some theory for kriging |
| title_exact_search | Interpolation of spatial data some theory for kriging |
| title_full | Interpolation of spatial data some theory for kriging Michael L. Stein |
| title_fullStr | Interpolation of spatial data some theory for kriging Michael L. Stein |
| title_full_unstemmed | Interpolation of spatial data some theory for kriging Michael L. Stein |
| title_short | Interpolation of spatial data |
| title_sort | interpolation of spatial data some theory for kriging |
| title_sub | some theory for kriging |
| topic | Krigeage Minerais - Echantillonage et estimation ram Stochastische processen gtt Kriging Kriging (DE-588)4339232-5 gnd |
| topic_facet | Krigeage Minerais - Echantillonage et estimation Stochastische processen Kriging |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008620272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT steinmichaell interpolationofspatialdatasometheoryforkriging |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 627f 2001 A 1228
Lageplan 0102 MAT 627f 2005 A 1228 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |
| Exemplar 3 | Ausleihbar Am Standort |