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Heyde C.C. — Quasi-likelihood and its application: a general approach to optimal parameter estimation |
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Предметный указатель |
Aalen, O.O. 18 19 150 166 211
Aase, K.K. 177 211
Abraham, B. 176 177 225
Acceptable estimating function 74
Adenstadt, R.K. 155 156 211
Aggoun, L. 136 138 214
Aitchison, J. 183 211
Algorithm 127 177
Algorithm, E—M 116—119 123 127
Algorithm, P—S 116—119 123 127
Ancillary 43 60 107.
Anderson, P.K. 18 211
Anh, V.V. 160 161 211
ARMA model 23
Asymptotic first order efficiency 72
Asymptotic mixed normality 27 60 62—64
Asymptotic normality 26 27 40 41 54—56 60 62—64 110 136 147 159 161 163 164 179 191 196 197 201
Asymptotic quasi-likelihood See quasilikelihood asymptotic
Asymptotic relative efficiency 74 125 126 167 168 175
Asymptotically non-negative definite 71 72
Autoregressive process 19 23 31 56 79 98 170 173 174 176
Autoregressive process, conditional 137
Autoregressive process, random coefficient 176
Autoregressive process, spatial 137
Autoregressive process, threshold 176
Baddeley, A.J. 201 211
Bailey, N.T.J. 162 163 211
Banach space 147
Barndorff-Nielsen, O.E. 35 56 59 62 86 211
Basawa, I.V. 54 60 63 132 135 141 142 169 173 185 212
Becker, N.G. 165 168 212
Belyea, C. 200 215
Beran, J. 158 212
Berliner, L.M. 37 212
Bernoulli distribution 87
Besag, J.E. 91 212
Best linear unbiased estimator (BLUE) 153 154
Beta distribution 124
Bhapkhar, V.P. 115 212
Bias correction 61 67
Bibby, B.M. 135 212
Billingsley, P. 65 212
Binary response 25
Binomial distribution 122 167
Birth and death process 18
Birth process 56
Black — Scholes model 31
Bootstrap 9 210
Borgan, O. 18 211
Bradley, E.L. 7 212
Branching process 182
Branching process, Galton — Watson 2 15 27 31 35 36 69 87 195
Brockwell, P.J. 60 212
Brouwer fixed point theorem 183
Brownian motion 17 31 33 34 131—133 136 196
Burkholder, Davis, Gundy inequality 149
Bustos, O.H. 169 213
Cadlag 191
Carroll, R.J. 131 139 203 205 213 214 225
Cauchy distribution 40 200
Cauchy — Schwarz inequality 5 24 167
Censored data 150
Central limit results 4 9 26 27 64 149 155 166 167 179 190—195
Chan, N.H. 56 213
Chandrasekar, B. 19 213
Characteristic function 199
Chebyshev inequality 189
Chen, K. 88 213
Chen, Y. 182 213
Cheng, R.C.H. 54 213
Chi-squared distribution 58 110 143—145 172
Choi, Y.J. 163 213
Cholesky square root matrix 71 72
Chung, K.L. 97 213
Coefficient of variation 121 124
Colloidal solution 69
Comets, F. 179 213
Complete probability space 92
Conditional centering 179
Conditional inference 107
Confidence intervals (or zones) 1 4 8 9 24 27 53—67 69 71 88 110 131 158 163 171 191 210
Confidence intervals (or zones), average 56 66
Confidence intervals (or zones), simulteneous 58
Consistency 6 8 10 26 38 40 54 55 63 64 70 131 135 147—150 161 163 179—186 190 196 197 201 203
Constrained parameter estimation 8 107—112 142
Control 41
Convergence, mixing 57 191 192
Convergence, stable 191 193 195
Convex 14 46 156—158
Correlation 6 13 25
Counting process 18 112 150 151 165
Covariate 25 148
Cox — Ingersoll — Ross model 131 133
Cox, D.R. 35 41 54 58 61 62 107 180 211 213
Cox, J.S. 131 133 213
Cramer — Rao inequality 2 7
Cramer — Wold device 195
Cramer, H. 2 7 180 185 195 213
Cross-sectional data 159
Crowder, M. 95 105 213
Cumulant spectal density 159
Cumulative hazard function 9 150
Curvature 62
Cutland, N.J. 31 213
Dahlhaus, R. 86 214
Daley, D.J. 156 214
Davidian, M. 131 214
Davis, R.A. 19 214
Demographic stochasticity 36
Dempster, A.P. 116 214
Denby, L. 169 214
Desmond, A.F. 2 25 214
Determinant criterion for optimality 19
Differentiability (stochastic) 56
Differential geometry 62
Diffusion 8 17 129 131 132 135 148 151 200
Dion, J.-P. 10 214
Discrete exponential family 2 16
dispersion 12 22 119 124 129
Distance 7 12
Doob — Meyer decomposition 27
Doukhan, P. 179 214
Drift coefficient 131 148
Duffie, D. 31 214
Durbin, J. 1 214
Dynamical system 37 38 40 131 136
E-ancillary 8 43—51 113 114
E-sufficient 8 43—51 113 114
Edgeworth expansion 62
Efficient score statistic 9 141 142
Efron, B. 59 214
Eigenfunction 200 201
Eisenberg, B. 155 211
Elliott, R.J. 50 136 138 214
Ellipsoids (of Wald) 58
Epidemic 9 162 163
Equicontinuity (stochastic) 56
Ergodic 134 142 153
Ergodic theorem 134 153 208
Error, approximation 148 151
Error, contrasts 139
Error, estimation 148 151
Estimating function space 3—5 8 11 13 15—19 22—25 28 32 36—40 43—51 71 75 88 89 92 94—96 99 100 104 105 111 130 132 137 138 153 162—164 166 169—171 176 195 199—201
Estimating functions 1 2
Estimating functions space, convex 14 46—48
Estimating functions space, Hutton — Nelson 32 33 162—164
Estimating functions, combination 2 8 35 103 137 138
Estimating functions, optimal 4—6
Estimating functions, robust 9 169—175
Estimating functions, standardized 3—5 118 138
| Estimation, constrained parameter 8 107—112 142
Estimation, function 147—151
Estimation, recursive 176—177
Estimation, robust 169—175
Euclidean space 11 92 94 141 182
Euler scheme 151
Exponential distribution 41 121 125
Exponential family 2 7 16 24 38 53 79 125
E—M algorithm 8 103 107 116 117 119—123 127
F-distribution 110
Failure 38
Feigin, P.D. 17 200 214 215
Fejer kernel 157
Ferland, R. 10 214
Field See random field
Filtering 8 103
Filtration 27 30 54 94 132
finance 31 135
Finite variation process 31 148
First order efficient 72 73
Firth, D. 61 67 95 102 105 215
Fisher information 2 12 40 59 72 141
Fisher information, conditional 97
Fisher method of scoring 120 202
Fisher, R.A. 1 2 12 40 59 72 97 107 141 202
Fitzmaurice, G.M. 25 26 215
Fourier methods 85
Fox, R. 86 215
Fractional Brownian motion 31 86
Fuerth, R. 87 215
Function estimation 9 147—151
Functional relationships 112 205
Galton — Watson process 2 15 27 31 36 69 195
Gamma distribution 56 134
Gastwirth, J.L. 169 215
Gauss — Markov theorem 3 4 161
Gauss, C.F. i 1 3 25 83 84 86 127 138 158 159 161 215
Gaussian distribution 83 86 127 138 158 159.
Gay, D.M. 202 215
Gay, R. 74 82 88 218
Generalized estimating equation (GEE) 8 25 26 89
Generalized inverse 30 108 109 130 132 184
Generalized linear model (GLIM) 21 22 79 100 104 202
Geometric distribution 38
Gibbs field 138
Gibbs sampler 201
Gill, R.D. 18 211
Girsanov transformation 138
Glynn, P. 64 215
Godambe, V.P. 1 2 21 38 48 97 105 107 116 172 215 216
Gram — Schmidt orthogonalization 93 96
Greenwood, P.E. 56 216
Grenander, U. 147 156 216
Guyon, X. 179 201 216
Hajek convolution theorem 63
Halfin, S. 157 216
Hall, P. 54 57 63 87 156 180 181 187 192 195 216
Hanfelt, J.J. 203 216
Hannan, E.J. 83 85 86 153 216 217
Harris, I.R. 102 215
Harville, D. 130 217
Hazard function 150
Hermite — Chebyshev polynomials 97
Heteroscedastic, autoregression 79
Heteroscedastic, regression 9 159—161
Heyde, C.C. 1 2 13 38 48 54 57 62 63 69 72 74 82 87 88 92 94 97 107 116 126 131 136 153 156 159 161 165 168 169 172 180 181 187 192 195 203 212 213 216—218 220 222
Hidden Markov models 9 93 136 139
Hilbert space 13 44
Hinkley, D.V. 35 41 54 58 59 61 107 180 213 214
Hoffmann — Jorgensen, J. 56 218
Holder inequality 86
Hotelling, H. 13 218
Huber function 173
Huber, P.J. 169 173 219
Huggins, R.M. 169 173 212
Hutton — Nelson estimating function 32—36 150 151 162—164 196
Hutton, J.E. 32—36 56 61 97 150 151 162—164 184 191 196 219
Hypothesis testing 9 141—145
Ibragimov, I.A. 155 219
Idempotent matrix 99 100 143
Iglehart, D.L. 64 215
Immigration distribution 69 70 87
Infection rate 9 162
Infectives 162 164
Infinitesimal generator 9 200 201
information 2 7 8 12 40 41 55 72 92 108 113 114 118 126 142 159
Information, empirical 59 204
Information, expected 59 204
Information, Fisher 2 12 40 59 72 97 141
Information, martingale 28 96—98 160 166 167 172
Information, observed 59
Ingersoll, J.E. 131 133 213
Integration by parts 190
Intensity 18 34 56 135 148 165
Interest rate 133
Invariance 2 58
Ito formula 32 97 135 194
Jackknife 9 210
Janzura, M. 179 213
Jensen inequality 66
Jiang, J. 131 219
Judge, G.G. 111 219
Kabaila, P.V. 85 87 219
Kale, B.K. 2 19 211 216
Kallianpur, G.K. 33 148 219
Kalman filter 8 103
Karlin, S. 200 219
Karr, A. 148 219
Karson, M.J. 130 219
Kaufmann, H. 186 219 220
Keiding, N. 18 211
Kernel estimation 147
Kessler, M. 135 200 201 220
Kimball, B.F. 1 220
Kloeden, P.E. 134 135 151 220
Koch, R.W. 197 223
Kopp, P.E. 31 213
Kronecker lemma 190
Kronecker product 80
Kulkarni, P.M. 169 220
Kulperger, R. 85 220
Kunita — Watanabe inequality 50
Kunsch, H. 169 210 220
kurtosis 62 98 104 130 139
Kutoyants, Yu. 62 220
Lagrange multiplier 108 111—113
Lahiri, S.N. 208 220
Laird, N.M. 25 26 116 122—124 212 215 220
Langevin model 131 135
Laplace transform 200
Laplace, P.S. de 1
Lattice 81 136
Law of Large Numbers 120 204 205 207 208.
Le Cam, L. 53 58 220 221
Least squares 1 2 3 5 7 10 21 87 161 202—205 209
Lee, Y. 23 223
Legendre, A. 1
Lele, S. 37 38 210 221
Lepingle, D. 187 196 221
Leskow, J. 148 221
Lexicographic order 101
Li, B. 62 142 180 203 221
Liang, K.Y. 21 25 221 226
Lifetime distribution 150
Likelihood 6 8 10 16 25 35 40 41 53 54 58 72 83 91 111 117 118 122 123 127 129 133 138 141 142 165 179 180 184 202 203
Likelihood ratio 58 63 131 134 141 142 145 203
Likelihood, conditional 107
Likelihood, constrained 0
Likelihood, non-regular cases 40 41
Likelihood, partial 107
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