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| Bloomfield P., Steiger W. — Least Absolute Deviations |
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| Предметный указатель |
Abdelmalek, N.N. 33 272 273
Algorithms for LAD fitting 181
Amemiya, T. 73 74
An, H.-Z. 34 108
Anderson, D. 33 171 220 231 234
Andrews, D.F. 270
Armstrong, R.D. 33 34 111 112 201 218 231 232 263 272 274
Ashar, V.G. 34
Asymptotic normal distribution see also "Central limit theorem"
Autoregression 77
Autoregression, existence of 79
Autoregression, LAD estimator for BO 102 105
Autoregression, LAD estimator for, consistency of 82 84 96 107
Autoregression, LAD estimator for, sampling behavior of 98
Autoregression, least squares estimator for 80 102 105
Autoregression, least squares estimator for, consistency of 107
Autoregression, M estimator for 103 106
Autoregression, stationarity condition for 77
Avis — Chvatal linear program 169 173
Avis, D. 169 175
Barrodale — Roberts algorithm 186
Barrodale — Roberts algorithm, data structure for 186 197
Barrodale — Roberts algorithm, formal statement of 194
Barrodale — Roberts algorithm, startup phase of 186
Barrodale, I. 33 34 183 186 196 197 199 220 271 272 273 274
Bartels — Conn — Sinclair algorithm 202
Bartels — Conn — Sinclair algorithm, data structure for 208
Bartels — Conn — Sinclair algorithm, formal statement of 206
Bartels, R.H. 11 33 34 179 180 183 186 202 273
Basic feasible solution 154
Basic variable 154
Bassett, G. 34 50 73 75 138
Beaton, A. 259
Belsley, D.A. 76
Ben-Israel, A. 33 161 179 271 272 273
Billingsley, P. 49
Bloomfield — Steiger algorithm 212
Bloomfield — Steiger algorithm, comparison with Seneta — Steiger algorithm 253
Bloomfield — Steiger algorithm, data structure for 216
Bloomfield — Steiger algorithm, formal statement of 216
Bloomfield — Steiger algorithm, startup phase of 212
Bloomfield, P. 35 145 183 186 212 273
Boscovitch, R.J. 2 3
Bounded variable linear program 161 271
Boundedness of set of LAD fits 13
Breakdown point of location estimator 52
Breakdown point of regression estimator 53
Carlson, D. 34
Carroll, R.J. 74
Cauchy distribution 96
Cauchy, A.L. 238
Central limit theorem for LAD estimator for linear model 44
Central limit theorem for least squares estimator 50
Central limit theorem for R estimator 64
Chambers, J.M. 36
Characterization of LAD fits 5 6 7 21 23 24 26 31
Charnes, A. 179 182
Check function 137
Chen, Z.-G. 34 108
Chvatal, V. 159 169 175 178
Clark, D. 185 259 269 270
Computational complexity 5
Computational complexity of LAD fitting 166 231
Computational complexity of linear programming 166
Computational complexity of simplex method 167 168
Computational complexity, comparison of Bloomfield — Steiger and Seneta — Steiger algorithms 253
Conditional median 139
Conditional quantile 138 139
Conn, A. 179
Conn, A.R. 11 33 34 183 186 202 273
Consistency of LAD estimator for autoregression 82 84 96 107
Consistency of LAD estimator for linear model 41 73
Consistency of least squares estimator 75
Consistency of least squares estimator for autoregression 107
Constrained fit 3 271 273
Contaminated normal distribution 65 99
Continuation algorithm for Huber M estimator 266
Continuation algorithm for Huber M estimator, formal statement of 268
Continuity of LAD criterion 12
Convergence of LAD criterion 39
Convexity of LAD criterion 12 40
Convexity of set of LAD fits 18 20
Cook, R.D. 57 76
Cooper, W.W. 179 182
Cox, D.D. 150
Craven, P. 151
Curve fitting 1
Daniel, C. 270
Dantzig, G. 167 170 178
Data structure for Barrodale — Roberts algorithm 186 197
Data structure for Bartels — Conn — Sinclair algorithm 208
Data structure for Bloomfield — Steiger algorithm 216
Data structure for linear program 160
Data structure for Seneta — Steiger algorithm 246
Davies, M. 34 271
de Boor, C. 144 145
Dead point 205
Degeneracy of LAD fits 6 11 35
Degenerate point 20
Dense linear program 172
Dinkel, J.J. 34
Distribution, Cauchy 96
Distribution, contaminated normal 65 99
Distribution, double exponential 39 65
Distribution, least informative 66
Distribution, logistic 65
Distribution, normal 65 104
Distribution, Pareto 66 67 99 100 226 231
Distribution, stable 74
Distribution, stable, domain of attraction of 75 81 84 98 105 107
Domain of attraction of stable distribution 75 81 84 98 105 107
Donoho, D. 52
Double exponential distribution 39 65
Dual objective function 160
Dual variable 160
Duality theorem of Linear Programming 159 344
Dunham, J.R. 171
Dutter, R. 261
Edge direction 30
Edge set 30
Edgeworth, F.Y. 6 10 11 181
Effects in multi-way table 109 121
Eisenhart, C. 2
Elam, J.J. 34
Ellipsoidal shrinking method 166
Emerson, J.D. 121 129
Equivariance 111
Ergodic sequence 39
Estimator see also "LAD estimator" "Least "M "Maximum "R
Existence of autoregression 79
Existence of LAD fits 13
Extent of set of LAD fits 19
Extreme LAD fits 35
Extreme point 19
Fair, R.C. 263
Feasible problem 152
Feasible region 152 153
Feasible solution 152
Feasible solution, basic 154
Feller, W. 75 107
Ferguson, R.O. 179 182
Fisher information 64 66
Fisher, L. 113
Fisher, W.D. 262
Fourier, J. 178
Frome, E.L. 34 111 112 201 218 231 232 263 274
Gacs, P. 166
Gallant, A.R. 34 263
Gauss, C.F. 7 8 10 238
Gaussian distribution see also "Normal distribution"
| Gentle, J.E. 34 35
Gerig, T.O. 34 263
Gilsinn, J. 274
Godfrey, J. 33 272
Goodall, C. 146
Gradient, normalized 215 244
Gradient, projected 202 203 273
Gross, S. 34 73 107
Grotschel, M. 167
Half-step of median polish 120
Hampel, F. 56
Hannan, E.J. 80 81 107
Harris, T. 34 179 182
Hoaglin, D.C. 121 129
Hoffman, K. 274
Hogg, R.V. 75
Holland, P. 263
Huber, P.J. 56 66 69 131 145
Hultz, J.W. 34 274
Hyperplane 1
Hyperplane, optimal 7 52
Influence function 56
Influence function of LAD estimator 58 59
Influence of data points 56
Interaction-free decomposition of two-way table 116 119
intercept 1 35 43 61 62 63
Interpolation 132
Interval program 161 271
Iteratively reweighted least squares algorithm 258
Iteratively reweighted least squares algorithm for splines 144
Iteratively reweighted least squares algorithm formal statement of 260
Jackson, R.H.F. 274
Jaeckel, L. 60 64 75
Jeroslow linear program 168
Jeroslow, R.G. 168 179
Johnson, N.L. 110
Kanter, M. 34 74 75 80 81 107
Kantorovitch, L.V. 178
Karst, O.J. 11 34 271
Kelly, D.G. 171
Kemperman, J. 126 129
Kennedy, W.J. 34 35
Khachian, L.G. 166 167
Kiountouzis, E. 33 272
Klee — Minty linear program 167
Klee, V. 167
Knot 131 140
Knuth, D.E. 36 211
Koenker, R. 50 73 75 138
Kohler, D.A. 178
Krasker, W.S. 76
Kuh, E. 76
Kuhn, H. 169 170
Kung, D.S. 201 218 232 274
LAD criterion, continuity of 12
LAD criterion, convergence of 39
LAD criterion, convexity of 12 40
LAD estimator for autoregression 80 102 105
LAD estimator for autoregression, consistency of 82 84 96 107
LAD estimator for autoregression, sampling behavior of 98
LAD estimator for linear model 38
LAD estimator for linear model, central limit theorem for 44
LAD estimator for linear model, consistency of 41 73
LAD estimator for linear model, sampling behavior of 64
LAD estimator for multi-way table, statistical properties of 117
LAD estimator, statistical properties of 39
LAD fits for multi-way table 110
LAD fits for multi-way table, uniqueness of 112
LAD fits for one-way table 110
LAD fits for one-way table, uniqueness of 110
LAD fits for two-way table 115 116 123 124
LAD fits for two-way table, uniqueness of 128
LAD fits, boundedness, of set of 13
LAD fits, characterization of 5 6 7 21 23 24 26 31
LAD fits, constrained 3 271 273
LAD fits, convexity of set of 18 20
LAD fits, degeneracy of 6 11 35
LAD fits, existence of 13
LAD fits, extent of set of 19
LAD fits, extreme 35
LAD fits, uniqueness of 6 10 21 23 26
LAD fitting problem 1
LAD fitting, algorithms for 181
LAD fitting, computational complexity of 166 231
LAD fitting, connection with linear program 271
LAD fitting, connection with linear programming 152 158
LAD fitting, data structure for 186 197 208 216 246
LAD fitting, equivalent linear program 161 163 164 165
LAD fitting, Monte Carlo experiment for 220 254
LAD residuals, signs of 16
LAD spline 135
LAD spline, generalized 137 140
Lagrange multiplier 29
Lai, T.L. 75
Laplace, P.-S. 3 5 6
Laurent, P.J. 135 141
Least informative distribution 66
Least squares estimator 67 see
Least squares estimator for autoregression 80 102 105
Least squares estimator for autoregression, consistency of 107
Least squares estimator, central limit for 50
Least squares estimator, consistency of 75
Least squares spline 142
Legendre, A.M. 2
Leone, F.C. 110
Leyendecker, E. 274
Likelihood function 39
Linear model 37
Linear model, LAD estimator for 38
Linear model, LAD estimator for, central limit theorem for 44
Linear model, LAD estimator for, consistency of 41 73
Linear model, LAD estimator for, sampling behavior of 64
Linear model, Monte Carlo experiment for 64
Linear program see also "Simplex method"
Linear program, Avis — Chvatal example 169 173
Linear program, basic feasible solution of 154
Linear program, basic variable in 154
Linear program, bounded variable 161 271
Linear program, characteristic form for LAD fitting 161 163 164 165
Linear program, computational complexity of 166
Linear program, connection with LAD fitting 152 158 271
Linear program, data structure for 160
Linear program, dense coefficients 172
Linear program, dual objective function of 160
Linear program, dual variable of 160
Linear program, duality theorem for 159
Linear program, ellipsoidal shrinking method for 166
Linear program, feasible 152
Linear program, feasible region of 152 153
Linear program, feasible solution of 152
Linear program, interval 161 271
Linear program, Jeroslow example 168
Linear program, Klee — Minty example 167
Linear program, Monte Carlo experiment for 169 174
Linear program, objective function of 152
Linear program, optimal solution of 152
Linear program, slack variable in 153 159 160
Linear regression 37
Local quantile 141
Loeve, M. 45 88
Logistic distribution 65
Lovasz, L. 166 167
Low median 125
Low median polish 125
M estimator 60 61 67 102 259 264 see
M estimator for autoregression 103 106
M estimator, Huber 68
Marcinkiewicz, J. 45 88
Maronna, R 107
Maximum likelihood 39 67 102
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