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Bloomfield P., Steiger W. — Least Absolute Deviations
Bloomfield P., Steiger W. — Least Absolute Deviations



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Название: Least Absolute Deviations

Авторы: Bloomfield P., Steiger W.

Аннотация:

In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1983

Количество страниц: 349

Добавлена в каталог: 12.04.2010

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