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| Khuri A.I. — Advanced calculus with applications in statistics |
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| Предметный указатель |
Quadratic form 39
Quadratic form, extrema of 48
Quadratic form, nonnegative definite 40
Quadratic form, positive definite 40
Quadratic form, positive semidefinite 40
Quadrature 524
Quadrature, Gauss — Chebyshev 526
Quadrature, Gauss — Hermite 528 542
Quadrature, Gauss — Jacobi 526
Quadrature, Gauss — Laguerre 528
Quadrature, Gauss — Legendre 526
Raabe’s test 155
Radius of convergence 174
Random effects 44
Random variable 13
Random variable, absolutely continuous 116 239
Random variable, Bernoulli 194
Random variable, binomial 14 203
Random variable, chi-squared 246
Random variable, continuous 14 82 116 239
Random variable, discrete 14 182
Random variable, function of 116
Random variable, normal 245
Random variable, Poisson 14 124 183
Random vector 304
Random vector, transformations of 305
Range of a function 5
Rank of a matrix 33
Ratio Test 148
Rational number 8
Rayleigh’s quotient 41
Rayleigh’s quotient, infimum of 41
Rayleigh’s quotient, supremum of 41
Rearrangement of series 159
refinement 206 214 294
Region of convergence 174
Relation 4
Relation, congruence 5
Relation, equivalence 4
Relation, reflexive 4
Relation, symmetric 4
Relation, transitive 4
Remainder 110 257 279
Response surface design 339 355 359
response surface methodology 339 355 367 504
Response variable 121
Response, constrained 352
Response, maximum 340
Response, minimum 340
Response, optimum 350
Response, predicted 341 344 355 504
Response, primary 352
Response, surface 340
Restricted least squares 429
Ridge analysis 343 349 352
Ridge analysis, modified 350 354
Ridge analysis, standard 354
Ridge estimator 56 196
Ridge plots 346
Ridge regression 195
Riemann integral 206 293
Riemann integral, double 295
Riemann integral, iterated 295
Riemann integral, n-tuple 295
Riemann — Stieltjes integral 234
Risk function 86
Rodrigues formula 440 443 447 451
Rolle’s Theorem 99 110
Root test 149
Rotatability 347
Saddle point 114 284 344 349
Saddlepoint approximation 549
Sample 14
Sample space 13
Sample variance 14
Satterthwaite’s approximation 324
scalar 21
Scalar, product 23
Scheffe’s confidence intervals 382 384
Schur’s Theorem 42
SEQUENCE 132 262
Sequence, bounded 132 262
Sequence, Cauchy 138 222
Sequence, convergent 133 262
Sequence, divergent 133
Sequence, limit infimum of 136 148 151
Sequence, limit of 133
Sequence, limit supremum of 136 148 151
Sequence, monotone 133
Sequence, of functions 165 227
Sequence, of matrices 178
Sequence, of orthogonal polynomials 437
Sequence, subsequential limit of 136
Sequence, uniformly convergent 166 169 228
Series 140
Series, absolutely convergent 143 158 174
Series, alternating 158
Series, conditionally convergent 158
Series, convergent 141
Series, divergent 141
Series, Fourier 471
Series, geometric 142
Series, Gram — Charlier 457
Series, harmonic 145
Series, hypergeometric 157
Series, Maclaurin’s 111
Series, multiplication of 162
Series, of functions 165
Series, of matrices 178 180
Series, of positive terms 144
Series, power 174
| Series, rearrangement of 159
Series, sum of 140
Series, Taylor’s 111 121
Series, trigonometric 471
Series, uniformly convergent 166 169
Set(s) 1
Set(s), bounded 9 72 262
Set(s), closed 11 72 262
Set(s), compact 13
Set(s), complement of 2
Set(s), connected 12
Set(s), convex 79
Set(s), countable 6
Set(s), covering of 12
Set(s), disconnected 12
Set(s), empty 1
Set(s), finite 6
Set(s), image of 5
Set(s), open 10 262
Set(s), partition of 5
Set(s), subcovering of 13
Set(s), uncountable 7
Set(s), universal 2
Sherman — Morrison formula 54
Sherman — Morrison — Woodbury formula 54 389
Simplex method 332
Simpson’s method 521
Simulated annealing 338
Simultaneous diagonalization 40
Singular values of a matrix 46
Singular-value decomposition 39 45
Singularity of a function 225
Size of test 15
Spectral decomposition theorem 38 181 351
spherical polar coordinates 322
Spline functions 418 428
Spline functions, approximation 418 421
Spline functions, cubic 419 428
Spline functions, designs for 430
Spline functions, error of approximation by 421
Spline functions, linear 418
Spline functions, properties of 418
Squared error loss 86
Stationary point 284 345
Stationary value 113
Statistic 14
Statistic, first-order 20
Statistic, Hotelling’s  49
Statistic, nth-order 20
Steepest ascent, method of 330 340
Steepest ascent, path of 396
Steepest descent, method of 329
Steepest descent, path of 343
Step function 237
Stieltjes moment problem 185
Stirling’s formula 532
Stratified sampling 313
Stratum 313
SubMatrix 29
Submatrix, leading principal 29
Submatrix, principal 29
Subsequence 135 262
Subsequential limit 136
Subset 1
Supremum 9 73
Symmetric difference 17
t distribution 259
Taylor’s Formula 110
Taylor’s series 111 121
Taylor’s series, remainder of 110 257 279
Taylor’s Theorem 108 114 277
Time series 500
Topological space 10
topology 10
Topology, basis for 10
Total derivative 270
Transformation, Box and Cox 120
Transformation, of continuous random variables 246
Transformation, of random vectors 305
Transformation, variance stabilizing 118
Translation invariance 379
Trapezoidal method 517
Triangle inequality 25
Trigonometric polynomial(s) 495 500 504
Trigonometric series 471
Two-way crossed classification model 43 401
Uncountable set 7
Uniform convergence of sequences 166 169 228
Uniform convergence of series 167 169
Uniform distribution 83 92 116 250
Uniformly continuous function 68 74 82 265 407
union 2
Universal set 2
Upper limit 136
Upper semicontinuous function 90
Upper sum 206 294
Variance 117 239
Variance components 44 378
Variance criterion 359 366
Variance stabilizing transformation 118
Vector 21
Vector space 21
Vector space, basis for 23
Vector space, dimension of 23
Vector subspace 22
Vector, column 28
Vector, row 28
Vector, zero 21
Vronovsky’s theorem 410
Weierstrass approximation theorem 403
Weierstrass’s M-test 167 172
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