|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Khuri A.I. — Advanced calculus with applications in statistics |
|
|
|
| Предметный указатель |
Absolute error loss 86
Absolutely continuous function 91
Absolutely continuous random variable 116 239
Addition of matrices 29
Adjoint 34
Adjugate 34
Admissible estimator 86
Approximation of density functions 456
Approximation of functions 403 495
Approximation of integrals 517 533
Approximation of normal integral 460 469
Approximation of quantiles of distributions 456 458 468
Arcsin x 6 78
Asymptotic distributions 120
Asymptotically equal 66 147
Average squared bias 360 431
Average variance 360 400
Balanced mixed model 43
Behrens — Fisher test 324
Bernoulli sequence 14
Bernstein polynomial 406 410
Best linear unbiased estimator 312
beta function 256
Bias 359 360
Bias, criterion 359 366
Bias, in the model 359 366
Biased estimator 196
Binomial distribution 194
Binomial random variable 14 203
Bolzano — Weierstrass theorem 11
Borel field 13
Boundary 262 297
Boundary point 262
Bounded sequence 132 262
Bounded set 9 13 72 262
Bounded variation, function of 210 212
Bounds on eigenvalues 41
Box and Cox transformation 120
Box — Draper determinant criterion 400
Box — Lucas criterion 368 422 424—425
Calibration 242
Canonical correlation coefficient 56
Cartesian product 3 21
Cauchy criterion 137 221
Cauchy distribution 240
Cauchy sequence 138 222
Cauchy — Schwarz inequality 25 229
Cauchy’s condensation test 153
Cauchy’s mean value theorem 103 105 129
Cauchy’s product 163
Cauchy’s test 149
cell 294
Center-point replications 400
Central limit theorem 120 516
Chain rule 97 116
Change of variables 219 299
Characteristic equation 37
Characteristic function 505
Characteristic function, inversion formula for 507
Characteristic root 36
Characteristic vector 37
Chebyshev polynomials 415 444
Chebyshev polynomials, discrete 462
Chebyshev polynomials, of the first kind 444
Chebyshev polynomials, of the second kind 445
Chebyshev polynomials, zeros of 415 444
Chebyshev’s inequality 19 184 251 259
Chi-squared random variable 246
Christoffel’s identity 443
Closed set 11—13 72 262
Coded levels 347
Coefficient of variation 242
Cofactor 31 357
Compact set 13
Comparison Test 144
Complement of a set 2
Complement of a set, relative 2
Composite function 6 97 265 276
Concave function 79
Condition number 47
Confidence intervals, simultaneous 382 384 388
Consistent estimator 83
Constrained maximization 329
Constrained optimization 288
Constraints, equality 288
Continuous distribution 14 82
Continuous function 66 210 264
Continuous function, absolutely 91
Continuous function, left 68
Continuous function, piecewise 481 486 489 498
Continuous function, right 68 83
Continuous random variable 14 82 116 239
contrast 384
Controlled random search procedure 336 426
Convergence in distribution 120
Convergence in probability 83 191
Convergence in quadratic mean 191
Convergence, almost surely 192
Convex function 79 84 98
Convex set 79
Convolution 499
Cornish — Fisher expansion 460 468
Correlation coefficient 311
Countable set 6
Covering of a set 12
Covering of a set, open 12
Cubic spline regression model 430
Cumulant generating function 189
Cumulants 189 459
Cumulative distribution function 14 82 304
Cumulative distribution function, joint 14
Curvature, in response surface 342
Cylindrical data 505
Davidon — Fletcher — Powell method 331
Deleted neighborhood 57 262
Density function 14 116 239 304
Density function, approximation of 456
Density function, bivariate 305
Density function, marginal 304
Derivative 93
Derivative, directional 273
Derivative, partial 267
Derivative, total 270
Design measure, continuous 362
Design measure, discrete 363 366
Design,  factorial 340 358
Design,  factorial 358
Design,  -optimal 399
Design, A-optimal 365
Design, approximate 363
Design, Box — Behnken 359
Design, center 344 356
Design, central composite 347 353 358 400
Design, D-optimal 363 365 369
Design, dependence of 368—369 422
Design, E-optimal 365
Design, efficiency of 365
Design, exact 363
Design, first-order 340 356 358
Design, G-optimal 364
Design, matrix 356
Design, measure 362—363 365
Design, moments 362
Design, nonlinear model 367
Design, optimal 362 425
Design, orthogonal 358
Design, parameter-free 426
Design, Plackett — Burman 358
Design, points 353 360
Design, response surface 339 355 359
| Design, rotatable 350 356
Design, second-order 344 358
Determinant 31
Determinant, Hessian 276
Determinant, Jacobian 268
Determinant, Vandermonde’s 411
DETMAX algorithm 366
Diagonalization of a matrix 38
Differentiable function 94 113
Differential operator 277
Differentiation under the integral sign 301
Direct product 30 44
Direct search methods 332
Direct sum of vector subspaces 25
Direct sum, of matrices 30
Directional derivative 273
Discontinuity 67
Discontinuity, first kind 67
Discontinuity, second kind 67
Discrete distribution 14
Discrete random variable 14 182
Disjoint sets 2
Distribution, binomial 194
Distribution, Cauchy 240
Distribution, chi-squared 245
Distribution, continuous 14 82
Distribution, discrete 14
Distribution, exponential 20 91 131
Distribution, F 383—384
Distribution, gamma 251
Distribution, hypergeometric 463
Distribution, logarithmic series 193
Distribution, logistic 241
Distribution, marginal 304
Distribution, multinomial 325
Distribution, negative binomial 182 195
Distribution, normal 120 306 311 400
Distribution, Pearson Type IV 503
Distribution, Poisson 119 183 204
Distribution, power series 193
Distribution, t 259
Distribution, truncated Poisson 373
Distribution, uniform 83 92 116 250
Domain of a function 5
Dot product 23
D’Alembert’s test 148
Eigenvalues 36—37
Eigenvectors 37
EM algorithm 372 375
Empty set 1
Equal in distribution 15
Equality of matrices 28
Equivalence class 4
Equivalence theorem 365
Equivalent sets 5
Error loss, absolute 86
Error loss, squared 86
Estimable linear function 45 382 387
Estimation of unknown densities 461
Estimator, admissible 86
Estimator, best linear unbiased 312
Estimator, biased 196
Estimator, consistent 83
Estimator, least absolute value 327
Estimator, M 327
Estimator, minimax 86
Estimator, minimum norm quadratic unbiased 380
Estimator, minimum variance quadratic unbiased 382
Estimator, quadratic 379
Estimator, ridge 56 196
Euclidean norm 24 42 179 261
Euclidean space 21
Euler’s theorem 317
Event 13
Exchangeable random variables 15
Exponential distribution 20 91 131
Extrema, absolute 113
Extrema, local 113
F distribution 383—384
Factorial moment 191
Failure rate 130
Fisher’s method of scoring 374
Fixed effects 44
Fourier series 471
Fourier series, convergence of 475
Fourier series, differentiation of 483
Fourier series, integration of 483
Fourier, coefficients 472
Fourier, integral 488
Fourier, transform 497 507
Fubini’s Theorem 297
Function 5
Function of a random variable 116
Function, absolutely continuous 91
Function, bounded 65 72
Function, bounded variation 210 212
Function, composite 6 97 265 276
Function, concave 79
Function, continuous 67 210 264
Function, convex 79 84 98
Function, differentiable 94 113
Function, homogeneous 317
Function, implicit 273
Function, inverse 6 76 102
Function, left continuous 68
Function, limit of 57
Function, Lipschitz continuous 75 409
Function, loss 86
Function, lower semicontinuous 90
Function, monotone 76 101 116 210
Function, multivariable 261
Function, one-to-one 5
Function, onto 5
Function, periodic 473 489 504
Function, Riemann integrable 206 210 215
Function, Riemann — Stieltjes integrable 234
Function, right continuous 68 83
Function, risk 86
Function, uniformly continuous 68 74 82 265 407
Function, upper semicontinuous 90
Functionally dependent 318
Fundamental theorem of calculus 219
Gamma distribution 251
Gamma function 246 532
Gamma function, approximation for 532
Gauss — Markov theorem 55
Gaussian quadrature 524
Gauss’s test 156
Generalized distance approach 370
Generalized inverse 36
Generalized simulated annealing method, Generalized variance 363
Geometric mean 84 230
Geometric series 142
Gibbs phenomenon 514
Gradient 275
Gradient, methods 329
Gram — Charlier series 457
Gram — Schmidt orthonormalization 24
Greatest lower bound 9 72
Greatest-integer function 238
Harmonic frequencies 501
Harmonic mean 85
Harmonic series 145
Hazard rate 131
Heine — Borel theorem 13
Hermite polynomials 447
Hermite polynomials, applications of 456 542
Hermite polynomials, normalized 461
Hessian, determinant 276
Hessian, matrix 275 285 374
|
|
|
| Реклама |
|
|
|
|
|
О проекте