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Khuri A.I. — Advanced calculus with applications in statistics
Khuri A.I. — Advanced calculus with applications in statistics

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Название: Advanced calculus with applications in statistics

Автор: Khuri A.I.

Аннотация:

A graduate textbook for a two-semester course in advanced calculus and mathematical analysis. Khuri (statistics, University of Florida) reviews the concepts of set theory, limits, functions, differentiation, and infinite series, and presents some applications in statistics. The second edition adds three chapters on orthogonal polynomials, Fourier series, and approximation of integrals.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2002

Количество страниц: 700

Добавлена в каталог: 29.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $2^k$ factorial      340 358
Design, $3^k$ factorial      358
Design, $\Lambda_1$-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
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