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Bates Douglas M., Watts Donald G. — Nonlinear Regression Analysis and Its Applications (Wiley Series in Probability and Statistics)
Bates Douglas M., Watts Donald G. — Nonlinear Regression Analysis and Its Applications (Wiley Series in Probability and Statistics)

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Название: Nonlinear Regression Analysis and Its Applications (Wiley Series in Probability and Statistics)

Авторы: Bates Douglas M., Watts Donald G.

Аннотация:

A balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression. Provides background material on linear regression, including a geometrical development for linear and nonlinear least squares. The authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. Includes pseudocode for computing algorithms.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 384

Добавлена в каталог: 27.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abdollah, S.      306
Abruzzo, C.W.      74 273
Acceleration, array      236
Acceleration, in an arbitrary direction      239
Acceleration, normal      234
Acceleration, space dimension      234
Acceleration, tangential      234
Acceleration, vector      234
Accumulated data      96
Accumulated data, analysis by direct integration      98
Analysis of variance      29
Analysis of variance, nitrite example      110
Anderson, D.H.      172 182 282
Ansley, C.F.      23
Arcing      247
Armstrong, P.W.      69
Array, acceleration      236
Array, Hessian      233
Array, relative curvature      242
Array, second derivative      233
Array, transformation      251
Arrhenius relation      180 188
Assessing fit      23 26 29
Assessing fit, nitrite example      113 116
Assessing fit, nonlinear models      90
assumptions      23
Assumptions for least squares      5
Assumptions of correct model      24
Assumptions, additive disturbance      24 25
Assumptions, constant variance      25 26
Assumptions, disturbance      136
Assumptions, independence of disturbances      25
Assumptions, multiresponse      136
Assumptions, normal disturbances      25 91
Assumptions, planar      43 229 232 245 256
Assumptions, uniform coordinate      43 229 232 256
Assumptions, zero mean of disturbances      25
AUC (area under the curve)      180
Autocorrelation of residuals      93
Bache, C.A.      3 267
Bacon, D.W.      87 96 155 156
Bard, Y.      49 74 77 79 138 141 164 168
Bates, D.M.      49 86 141 144 145 147 171 178 217 233 244 246 249 254 255 259 260 261 300
Bayes, HPD region      7
Bayes, inference      7
Bayes, inference for nonlinear models      216
Beale, E.M.L.      225 232 233 261
Becker, R.A.      291
Belsley, D.A.      1 26
Bischoff, K.B.      168
Bliss, C.I.      205
Box, G.E.P.      1 3 7 24 27 28 42 70 81 93 94 122 123 124 125 127 131 134 135 137 138 139 140 147 148 155 156 157 161 213 218 220 261 272
Box, M.J.      125 129 164
Boyle, J.M.      316 317
Bright, P.B.      172 178
Brown, R.      310
Bunch, J.R.      13 81 145 156 244 289 295 302 316
Caracotsios, M.      68 69 168 179
Carr, N.L.      55 271
Carroll, R.J.      70 91
Chambers, J.M.      49 110 291
Chi-squared distribution      16
Chiong, M.A.      69
Cholesky decomposition      145
Cleveland, W.S.      110
Cochran, W.G.      123
Cole, K.S.      136
Cole, R.H.      136
Collinearity      78 80
Compansion      247
Compartment model      168
Compartment model, catenary      184
Compartment model, derivative with respect to parameter      178
Compartment model, mamillary      184
Compartment model, multiresponse estimation      188
Compartment model, practical considerations      179
Compartment model, sink      168
Compartment model, source      168
Compartment model, starting values      182
Compartment model, unidentifiable      181
Conditional likelihood      204
Conditionally linear model      129
Conditionally linear parameter      85
Confidence, band for response function      6 22
Confidence, geometry of interval      19 21
Confidence, geometry of region      17
Confidence, interval      6
Confidence, interval for expected response      6 22
Confidence, interval for parameter      21
Confidence, region      6
Confidence, region for nonlinear model      223
Constraint in multiresponse estimation      140
Constraint on parameter      77
Constraint, interval      77
Constraint, order      78
Conte, S.D.      69
Contour, likelihood      6 200
Contour, sum of squares      23 61
Convergence      40
Convergence, check      90
Convergence, criterion      49
Convergence, criterion for multiresponse estimation      145
Convergence, geometry      49
Convergence, orthogonality criterion      49
Convergence, practical considerations      86
Convergence, relative offset criterion      49
Convergence, to spurious optimum      154
Convergence, tolerance level      49
Convolution      173
Cook, R.D.      1 26 91
Correlation matrix      22
Correlation of residuals      92
Coutie, G.A.      261
Covariance matrix      5 137
Cox, D.R.      28 70
Cox, G.M.      123
Curvature, definition      241
Curvature, intrinsic      241
Curvature, measures of nonlinearity      232
Curvature, parameter effects      241
Curvature, root mean square (RMS)      254
D-optimal, design criterion      124
Daniel, C.      27
Davies, O.L.      123
Dead time      175 191
deBethizy, D.      96 274
deBoor, C.      69
Degrees of freedom      6 16
Degrees of freedom, extra parameter      103
Degrees of freedom, lack of fit      29
Degrees of freedom, replication      29
Degrees of freedom, residual      29
Dennis, J.E.Jr.      80 82 145
Dependencies in multiresponse data      154
Dependencies in multiresponse estimation      154 158
Derivative matrix      2 40 124 233
Derivative matrix, conditioning      78
Derivative of expectation function      71
Derivative, compartment model      178
Derivative, numerical      71
Derivative, vector      58
Determinant, constraints for multiresponse estimation      140
Determinant, criterion for multiresponse estimation      138
Determinant, design criterion      124 125
Determinant, evaluation by QR decomposition      141
Determinant, gradient of      142
Determinant, Hessian of      142
Determinant, Jacobian      12 38
Diagnostics      24 26
Differential equation, specification of nonlinear model      68
Disturbance, additive assumption      24
Disturbance, constant variance      25 26
Disturbance, independence      26
Disturbance, independent of expectation function      25
Disturbance, normal assumption      25
Disturbance, practical considerations      69
Disturbance, zero mean      25
Dongana, J.J.      13 81 145 156 244 289 295 302 316 317
Downie, J.      155 156
Draper, N.R.      vii 1 26 28 49 70 91 122 123 134 137 138 161 164
DUD      82
editing data      91
Edlefsen, L.E.      291
Ehrenberg, A.S.C.      110
Eigenvalue      173
Eigenvalue, analysis of centered data matrix      155
Eigenvector      173
Elliott, J.R.      110 278
Ellipse, approximation to sum of squares contour      63
Erjavec, J.      135 147 148 155 156 157 272
Estimate, least squares      5
Expectation function      2 25
Expectation function, correct model      24
Expectation function, linear approximation to      40 232
Expectation surface      36 38
Expectation surface, geometry      36
Expectation surface, linear approximation to      232
Expectation surface, prior density      217
Expectation surface, quadratic approximation      259
Expectation surface, tangent plane      232
Expectation, plane      10
Expectation, surface      9
Expected response      33
Expected response, confidence interval      6 22
Expected response, vector      10
Experimental design for conditionally linear model      129
Experimental design for linear expectation functions      124
Experimental design for nonlinear expectation functions      124
Experimental design, D-optimal      124
Experimental design, determinant criterion      124
Experimental design, general considerations      122
Experimental design, objectives      122
Experimental design, sequential      127
Experimental design, starting      125
Experimental design, subset      129
Extra determinant, test for nested models      162
Extra sum of squares and nonlinearity      104
Extra sum of squares, analysis for nested models      103
Extra sum of squares, nitrite example      116
F distribution      6 16
Fanning      247
Fedorov, V.V.      142
Fisher, R.A.      25
Froment, G.F.      168
Fuguitt, R.E.      68 135 157 165 272 310
Garbow, B.S.      316 317
Gauss increment      40
Gauss — Newton increment      81
Gauss — Newton, increment for multiresponse estimation      144
Gauss — Newton, iteration method      79
Gauss — Newton, method      40
Gauss — Newton, method for multiresponse estimation      143
Gay, D.M.      80
Gentle, J.E.      49
Geometry      36
Geometry of confidence region      17
Geometry of convergence      49
Geometry of experimental design determinant criterion      124
Geometry of likelihood approach      23
Geometry of linear least squares      9
Geometry of multiresponse determinant criterion      139
Geometry of nonlinear least squares      43
Geometry of nonlinear models      36
Geometry of sampling theory approach      15
Geometry of the expectation surface      36
Gill, P.E.      77
Godfrey, K.      168 180
Golub, G.H.      81 86 142
Gorman, J.W.      170 172 191 282
Gradient of determinant      142
Gradient of sum of squares function      79
Half-life      179
Halperin, M.      229
Hamilton, D.C.      69 123 228 234 244 259 260 261
Hartley, H.O.      42
Hat matrix      27
Havriliak, S.Jr.      136 146 149 280
Hawkins, J.E.      68 135 157 165 272 310
hessian      145
Hessian of determinant      139 142
Hessian of sum of squares function      61 80
Hessian, approximate      143
Hessian, array      233
Heyes, J.K.      310
Highest posterior density (HPD), approximate band in multiresponse estimation      140
Highest posterior density (HPD), approximate interval in multiresponse estimation      140
Highest posterior density (HPD), approximate region in multiresponse estimation      139
Highest posterior density (HPD), region      7
Highest posterior density (HPD), region for nonlinear model      220
Hill, P.D.H.      129 131
Hill, W.J.      129 131 213
Himmelblau, D.M.      49
Hinkley, D.V.      87
Hocking, R.R.      26
Hougen, O.A.      272
Hubbard, A.B.      170 188 282
Huber, P.J.      91
Hunter, J.S.      24 28 122
Hunter, W.G.      24 28 122 123 127 129 131 135 147 148 155 156 157 164 272
Hypothesis      17
Ikebe, Y.      316 317
Improving convergence, centering and scaling      78
Incremental parameter      91 104
Incremental parameter, nitrite example      113
Indicator variable      104
Indicator variable, nitrite example      110
Inference in multiresponse estimation      139
Inference in nonlinear regression      52
Inference, band, linear approximation      58
Inference, Bayes      7
Inference, interval, linear approximation      58
Inference, likelihood      6
Inference, linear approximation      52
Inference, linear approximation region      64
Inference, region      7 15
Inference, sampling theory      5
Intrinsic curvature      241
Intrinsic curvature, geometric interpretation      245
Intrinsic nonlinearity      237
Intrinsic nonlinearity, direct assessment      256 262
Intrinsic relative curvature array      242
Intrinsically linear model      34
Iteration      40
Jacobian      217
Jacobian, determinant      12 38
Jacobian, matrix      250
James, A.T.      205
Jenkins, G.M.      93 94
Jennrich, R.I.      49 82 85 172 178
Joiner, B.L.      27 91
Jones, S.D.      291
Jupp, D.L.B.      78 86
Juusola, J.A.      306
Kadane, J.B.      223
Kanemasu, H.      81
Kaplan, S.A.      74 273
Kaufman L.      86
Kennedy, W.J.Jr.      49
Khuri, A.I.      129 131
Kleiner, B.      110
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