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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
Lin, Y.-X.      43 88 105 159 186 218 221
Lindeberg — Feller theorem      4
Lindsay, B.      91 107 139 222
Linnik, Yu.V.      155 219
Liptser, R.S.      133 222
Little, R.J.A.      127 222
Liu, R.Y.      208 222
Loewner optimality      12 20
Loewner ordering      12 55 118 144
Logistic map      37 40
Logit link function      25
Long-range dependence      82 86 158 159
Longitudinal data      8 25
M-estimation      1 142
Mak, T.K.      202 222
Markov process      9 157 162 200 201
Markov, A.A. i      3 9 93 139 157 161 162 200 201
Martin, R.D.      169 172 214 222
Martingale      15 17 18 26—28 35 48 49 51 59 61 62 69 70 93 94—98 131—133 135 136 148—150 159 160 162—167 169—171 176 180 181 186—196 200 210
Martingale, central limit theorem      55 179 186 190—195
Martingale, continuous part      34 54
Martingale, information      See information martingale
Martingale, strong law      55 150 174 179 181 182 186—190 195 196
Maximum likelihood      1 2 16—19 21 34 35 38 39 41 53 54 57 58 61 70 92 98 116 124 129 131 134 136 141 148 160 163 165 166 169 180 200 202
Maximum likelihood, non-parametric      17
Maximum likelihood, regularity conditions      40 41 54 62
Maximum likelihood, restricted      141
McCormick, W.P.      19 214
McCullagh, P.      21 22 125 142 184 203 205 221 222
McKeague, I.W.      148 222
McLeish, D.L.      1 3 8 13 43—45 49 127 128 222 225
Measurement errors      139
Membrane potential      33 147
Merkouris, T.      13 199 223
Method of moments      1 153 154 156 169 202
Metric space      200
Minimal sufficient      1
Minimum chi-squared      1
Missing data      8 107 116 117 127
Mitra, S.K.      131 224
Mixed normality      27 62 63 192
Mixing conditions      84 156 179
Mixture densities      127
Models, branching      See branching process
Models, epidemic      162—164
Models, hidden Markov      93
Models, interest rate      133
Models, logistic      37 38 40
Models, membrane potential      33 147
Models, multi-stage      200
Models, nearest neighbour      91
Models, nested      99—102
Models, particles in a fluid      87
Models, physician services      127
Models, population      35—37
Models, queueing      157 158
Models, recapture      164—168
Models, risky asset      31
Models, soil moisture      196—197
Moment generating function      199
Moore — Penrose inverse      30
Moore, J.B.      136 138 214
Morton, R.      21 23 100—102 107 112 116 126 203 218 223
Moving Average      156 159 180.
Mtundu, N.D.      197 223
Multiple roots      202—209
Multiplicative errors      100 102
Mutual quadratic characteristic      26
Mykland, P.A.      62 223
Naik — Nimbalkar, U.V.      103 104 222
Nelder, J.A.      21 22 125 184 202 222 223
Nelson, P.I.      32—36 56 61 97 150 151 162—164 184 191 196 219
Nested strata      8 99
Neurophsiological model      32 147
Newton — Raphson method      202
Nguyen, H.T.      148 223
Noise      17 30 31 33 127 132 133 135 136
Noise, additive      36 37
Noise, multiplicative      36
Non-ergodic models      59 60 63 144
Nonparametric estimation      147 150
Norm (Euclidean)      55 71 184 186
Normal distribution      4 27 28 41 55—57 62—66 88 91 105 111 116 121 129—131 139 156 161 163 164 166 173
Nuisance parameter      8 57 59 60 70 71 88 107 113—115 139 159
Offspring distribution      16 27 69 70 87 182 195
Ogunyemi, O.T.      56 184 196 219
On-line signal processing      9 176
Optimal asymptotic (OA)      1 2 7 8 11 12 29 30
Optimal experimental design      8 12 20
Optimal fixed sample (OF )      1 5 7 11—21 28 30 55
Orthogonal      13 71 93 100 102—104 138 156 160
Orthonormal sequence      147
Osborne, M.R.      120 223
Outliers      169
Parameter space      41 43 50 53
Parameters, constrained      107—112 142
Parameters, incidental      112
Parameters, nuisance      See nuisance parameters
Parameters, scale      200
Parametric model      1 11
Partial likelihood      107
Parzen, E.      84 223
Pearson, K.      1
Pedersen, A.R.      135 223
Periodogram      82
Pham, D.P.      148 223
Pivot      66
Platen, E.      134 135 151 220
Point process      148. See also counting process Poisson
Poisson distribution      33 67 70 87 100 121 167
Poisson process      19 31 34 35 111 112 135 196 197
Poisson process, compound      35 196
Pollard, D.      56 223
Population process      35. See also branching process
Power series family      2 16
Prakasa — Rao, B.L.S.      54 132 135 141 212
Predictable process      18 31 51 94 97 162
Prediction variance      82
Pregibon, D.      202 223
Prentice, R.L.      25 224
Priestley, M.B.      84 224
Probability generating function      167
Projected estimating function      108—110 143
Projected estimator      13 108 143 144
Projection      13 47 107—109 114 125 129
Pukelsheim, F.      12 20 38 224
Purely nondeterministic      153
P—S algorithm      107 116
Qian, W.      136 224
Quadratic characteristic      27 29 59 94 132 144 151 166 187 192 196
Quadratic form      130
Quadratic variation process      33 54 133
Quasi-likelihood      1 7—9 12 16 18 19 21 22 36 38 40 53 61 69 70 73 87 107 116 121 129 130 131 134 138 139 142 147 148 150 151 160—165 169 180—182 195—197
Quasi-likelihood, asymptotic      8
Quasi-likelihood, composite      91 92
Quasi-score      7—9 12 13 22 23 26 35 39 43 46 48 50 51 55 58 62 67 69—72 80 82 83 85 87 92—96 98—100 102 104 105 108 109—112 116—118 122 125 127 128 130 132 134 135 137—139 142 144 145 154 159 162 163 166 170—173 175 176 179 182 195 196
Quasi-score, asymptotic      26 35 37 58 69 72—76 78—80 88 154
Quasi-score, combined      98 99 103 160
Quasi-score, conservative      142 203
Quasi-score, existence of      15 21 36—38
Quasi-score, Hutton — Nelson      33—36 61 150 151 162—164
Quasi-score, robust      170—174
Quasi-score, sub-      48 49
Queueing models      157 158
Radon — Nikodym derivitive      129 131—133
Rajarshi, M.B.      103 104 223
Random coefficient autoregression      176
Random effects model      105
Random environment      35 36
Random field      8 82 93 136 137 179 201
Random norming      8 56 63 189
Rao — Blackwell theorem      128
Rao, C.R.      2 7 20 28 29 72 73 95 108 128 129 131 141 224
Rebolledo, R.      166 224
Recapture experiment      9 164
Recursive estimation      9 176 177
Regression      9 21 23 25 60 89 111 113 148 159 170 173 174 205
REML estimation      8 129—131
Removal rate      164
Resampling      9 210
Residuals      99
Reynolds, J.F.      157 158 224
Riemann zeta function      126
Ripley, B.D.      137 224
Robust methods      9 169
Rogers, L.C.G.      26 31 54 133 149 224
Rosenblatt, M.      82 84 85 179 224
Rotnitzky, A.G.      25 26 215
Rozanski, R.      148 221
Rubin, D.B.      116 127 214 222
Rubin, H.      169 215
Samarov, A.      158 224
Sample space      2 43
Samuel, E.      165 224
Schuh, H.-J.      200 224
Score function      2 4 6—8 17 24 41 62 67 91 93 94 107 111 113 115—118 122 127 134 139 141 160 181 205
Scott, D.J.      63 142 185 212
Screening tests      122
Selukar, R.S.      148 219
Semimartingale      8 9 30—36 54 69 93 97 131 135 148
Semiparametric model      1 9
Seneta, E.      69 87 218
Service time      157
Severo, N.      163 213
Shen, X.      148 224
Shiryaev, A.N.      26 133 222 224
Short-range dependence      82 158 159
Shumway, R.H.      127 224
Sieve      9 147 148 151
signal      30—32 132 136
Silvey, S.D.      183 211
Simulation      64
Simultaneous reduction lemma      20 21
skewness      62 98 104
Slutsky theorem      65
Small, C.G.      1 3 8 13 43—45 49 127 128 222 225
Smith, R.L.      54 225
Smoothed periodogram      82
Smoothing      8 103 104
Smoothing function      82 84
Soil moisture      197
Sorensen, M.      34 35 56 59 135 136 191 197 200 201 212 220 225
Sources of variation      33—35 101 136 137 139
Spatial process      93
Spectral density      82 86 153 155 156 158 159
Square root matrix      71 72
Standardization      3—5 11 71
Standardized      64
State space models      103
Stationary process      1 153 156 158 210
Staudte, R.G.      169 173 212
Stefansky, L.A.      139 203 205 206 213 225
Stochastic differential equation      32 49 133 135 196 197
Stochastic disturbance      See noise
Stochastic integral      133 163
Stoffer, D.S.      127 224
Stopping time      189 193
Strata      99 100 102
Strong consistency      56 70 135 148 161 163 181 182 185 186 190 195
Structural relationships      112 206
Sufficiency      2 3 43.
Surrogate predictors      139
Sweeting, T.J.      60 225
Szegoe, G.      156 216
t-statistic      64 66 168
Takayama, T.      111 219
Taqqu, M.S.      86 158 215 224
Taylor, H.M.      200 219
Tchoukova-Dantcheva, S.      70 226
Thavaneswaran, A.      18 142 147 176 177 225
Thisted, R.A.      202 225
Thompson, M.E.      18 105 116 147 216 225
Time series      8 103 176
Titterington, D.M.      136 224
Toeplitz matrix      154
Trace criterion (for optimality)      19
Traffic intensity      158
Transform martingale families      199
Trapping rate      168
Traylor, L.      54 213
Treatment      4
Tweedie, R.L.      200 215 22
Unacceptable estimating function      74 75
Uniform convergence      57
Uniform distribution      41
Vajda, I.      180 226
Verbyla, A.P.      130 226
Vitale, R.A.      156 226
Vostrikova, L.      62 220
Wald test      9 141—143
Wald, A.      9 58 141—143 180 226
Watson, R.K.      162 226
Wedderburn estimating function      24
Wedderburn, R.W.M. i      7 21 23—25 101 226
Wefelmeyer, W.      56 216
Wei, C.Z.      56 70 87 211 226
Welsh, R.E.      202 215
Whittle estimator      83 86
Whittle, P. ii      82 83 86 226
Williams, D.      26 31 54 133 149 224
Williams, R.J.      97 213
Willinger, W.      31 213
Winnicki, J.      69 70 87 226
Wong, W.H.      148 224
Wu, C.F.J.      208 226
Yanev, N.M.      70 226
Yip, P.      162 226
Yohai, V.J.      169 172 222
Yule — Walker equations      23
Zeger, S.L.      21 25 200 226
Zehnwirth, B.      103 226
Zygmund, A.      157 226
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