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Heyde C.C. — Quasi-likelihood and its application: a general approach to optimal parameter estimation
Heyde C.C. — Quasi-likelihood and its application: a general approach to optimal parameter estimation

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Название: Quasi-likelihood and its application: a general approach to optimal parameter estimation

Автор: Heyde C.C.

Аннотация:

This is author-approved bcc: Quasi-likelihood is a very generally applicable estimating function based methodology for optimally estimating model parameters in systems subject to random effects. Only assumptions about means and covariances are required in contrast to the full distributional assumptions of ordinary likelihood based methodology. This monograph gives the first account in book form of all the essential features of the quasi-likelihood methodology,and stresses its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential princples rather than detailed proofs. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided. Readers are assumed to have a firm grounding in probability and statistics at the graduate level. Christopher Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He is a Fellow of the Australian Academy of Science and has been Foundation Dean of the School of Mathematical Sciences at the Australian National University and Foundation Director of the Key Centre for Statistical Sciences in Melbourne. He has served as President of the Bernoulli Society and Vice President of the International Statistical Institute and is Editor-in-Chief of the international probability journals "Journal of Applied Probability" and "Advances in Applied Probability". He has done considerable distinguished research in probability and statistics which has been honoured by the awards of the Pitman Medal (1988),Hannan Medal.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 236

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
1 2
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