Ãëàâíàÿ    Ex Libris    Êíèãè    Æóðíàëû    Ñòàòüè    Ñåðèè    Êàòàëîã    Wanted    Çàãðóçêà    ÕóäËèò    Ñïðàâêà    Ïîèñê ïî èíäåêñàì    Ïîèñê    Ôîðóì   
blank
Àâòîðèçàöèÿ

       
blank
Ïîèñê ïî óêàçàòåëÿì

blank
blank
blank
Êðàñîòà
blank
Schott J.R. — Matrix Analysis for Statistics
Schott J.R. — Matrix Analysis for Statistics



Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå



Íàøëè îïå÷àòêó?
Âûäåëèòå åå ìûøêîé è íàæìèòå Ctrl+Enter


Íàçâàíèå: Matrix Analysis for Statistics

Àâòîð: Schott J.R.

Àííîòàöèÿ:

A complete, self-contained introduction to matrix analysis theory and practice
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. As such, they have become a vital part of any statistical education. Unfortunately, matrix methods are usually treated piecemeal in courses on everything from regression analysis to stochastic processes. Matrix Analysis for Statistics offers a unique view of matrix analysis theory and methods as a whole.
Professor James R. Schott provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors, the Moore-Penrose inverse, matrix differentiation, the distribution of quadratic forms, and more. The subject matter is presented in a theorem/proof format, and every effort has been made to ease the transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, the text uses examples that are familiar and easy to understand. Other key features that make this the ideal introduction to matrix analysis theory and practice include:
- Self-contained chapters for flexibility in topic choice.
- Extensive examples and chapter-end practice exercises.
- Optional sections for mathematically advanced readers.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1996

Êîëè÷åñòâî ñòðàíèö: 431

Äîáàâëåíà â êàòàëîã: 21.10.2010

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
blank
Ïðåäìåòíûé óêàçàòåëü
Accumulation point      70
Adjoint      8
Analysis of variance      120 see "Two-way
Bartlett adjustment      406
Basis      41—43
Basis, orthonormal      48—52
Bilinear form      15
Block diagonal matrix      12
Boundary point      72
canonical variate analysis      107 154—155 406—407
Cauchy — Schwarz inequality      35
Cayley — Hamilton theorem      93
Chain rule      324 327
Characteristic equation      85
Characteristic root      84 see
Characteristic vector      84 see
Chi-squared distribution and Moore — Penrose inverse      179—180
Chi-squared distribution and quadratic forms      378—384
Chi-squared distribution, central      20—21
Chi-squared distribution, noncentra]      21
Cholesky decomposition      139
Circulant matrix      300—304
Closure      70
Cochran's theorem      374—378
Cofactor      5 8
Cofactor, expansion formula for determinant      5—6
Column space      43
Commutation matrix      276—283
Commutation matrix, eigenvalues      281
Commutation matrix, eigenvectors      317
Complex matrix      16—18
Concave function      see "Convex function"
Consistent equations      210—213
Consistent estimator      189—190
Continuity of determinant      188
Continuity of eigenvalues      103
Continuity of inverse matrix      188
Continuity of Moore — Penrose inverse      189
Convex combination      70
Convex function      349—353
Convex function, absolute maximum      352
Convex hull      70
Convex set      70—74
Correlation coefficient      24
Correlation coefficient, maximum squared      368
Correlation matrix      24
Correlation matrix, nonnegative definite      24
Correlation matrix, sample      25
Courant — Fischer min-max theorem      108—110
Covariance      22—23
Covariance matrix      23
Covariance matrix, nonnegative definite      23
Covariance matrix, sample      25
Covariance of quadratic forms      391 394
Decomposition, Cholesky      139
Decomposition, Jordan      147—149
Decomposition, LU      169
Decomposition, QR      140
Decomposition, Schur      149—153
Decomposition, singular value      131—138
Decomposition, spectral      95 98 138
Density function      19
Derivative      323 325
derivative of determinant      332 336
Derivative of eigenvalue      343
derivative of eigenvector      343
Derivative of inverse      333 336—337
Derivative of Moore — Penrose inverse      333—334 336—337
Derivative of patterned matrices      335—337
Derivative of trace      332
Derivative of vector function      327
Derivative, partial      325
Derivative, second-order partial      326
Determinant      5—8
Determinant and eigenvalues      90
Determinant of partitioned matrix      249—250
Determinant, continuity of      188
Determinant, derivative of      332 336
Determinant, expansion formula for      5—6
Diagonal matrix      2
Diagonalization      92 144—147
Diagonalization, simultaneous      118 154—157
Differential      324 325
Differential of determinant      332
Differential of eigenvalue      343
Differential of eigenvector      343
Differential of inverse      333 336—337
Differential of matrix function      328
Differential of Moore — Penrose inverse      334—335 336—337
Differential of trace      332
Differential of vector function      327
Differential, second      326
Dimension of vector space      41
Direct sum of matrices      260—261
Discriminant analysis      37
Distance function      36
Distance function, euclidean      36 50 62—63 141
Distance function, Mahalanobis      37 63 141
Distance in the metric of      37
Duplication matrix      238—285
Eigenprojection      98
Eigenprojection, continuity of      103
Eigenspace      87 146
Eigenvalue      84
Eigenvalue and rank      92 99 146—147 153
Eigenvalue in the metric of      118
Eigenvalue of idempotent matrix      370—371
Eigenvalue of orthogonal matrix      88
Eigenvalue of positive definite matrix      112
Eigenvalue of positive semidefinite matrix      112
Eigenvalue of symmetric matrix      93—102
Eigenvalue of transpose product      114—115
Eigenvalue of triangular matrix      88
Eigenvalue, asymptotic distribution of      404—406
Eigenvalue, continuity of      103
Eigenvalue, derivative of      343
Eigenvalue, distinct      86
Eigenvalue, extremal properties      104—110
Eigenvalue, monotonicity      115
Eigenvalue, multiple      86
Eigenvalue, perturbation of      339—343
Eigenvalue, simple      86
Eigenvectors      84
Eigenvectors of symmetric matrix      94—96
Eigenvectors, asymptotic distribution of      404—406
Eigenvectors, common      128 157
Eigenvectors, derivative of      343
Eigenvectors, linear independence of      91
Elementary transformations      13
Elimination matrices      285—288
Estimable function      230
Euclidean norm      36 37 158
Euclidean space      36
Euler's formula      17
Expected value      19
Expected value of quadratic form      390—398
F distribution      21—22
Fourier matrix      303—304
Gauss — Seidel method      236
Generalized inverse      190—196 see
Generalized inverse, computation of      200—203
Generalized inverse, properties      193
Gradient      237
Gram — Schmidt orthonormalization      48 54—55
Hadamard inequality      270
Hadamard matrix      305—307
Hadamard matrix, normalized      306
Hadamard product      266—276
Hadamard product as a Kronecker product      267
Hadamard product, eigenvalues of      274—276
Hadamard product, rank of      267
Hermite form      200
Hermitian matrix      18
Hessian matrix      326
Homogeneous system of equations      219—221
Hyperplane      71
Idempotent matrix      3 58—59 370—374
Idempotent matrix, eigenvalues of      370—371
Idempotent matrix, rank of      370—371
Idempotent matrix, symmetric      372 373—374
Idempotent matrix, trace of      370—371
Identity matrix      2
Indefinite matrix      16
Independence (linear)      38—40
Independence (stochastic) of quadratic forms      384—390
Independence (stochastic) of random variables      22
Inner product      34—35
Inner product, Euclidean      35
Interior point      72
Intersection of vector spaces      67
Inverse matrix      8—11
Inverse matrix and cofactors      8—9
Inverse matrix of a sum      9—10
Inverse matrix of partitioned matrix      347
Inverse matrix, continuity of      188
Inverse matrix, derivative of      333 336—337
Irreducible matrix      294—295
Jacobi method      236
Jacobian matrix      327
Jensen's inequality      352—353
Jordan decomposition      147—149
Kronecker product      253
Kronecker product, determinant of      256
Kronecker product, eigenvalues of      255
Kronecker product, eigenvectors of      312
Kronecker product, inverse of      255
Kronecker product, Moore — Penrose inverse of      255
Kronecker product, rank of      257
Kronecker product, trace of      255
Lagrange function      354
Lagrange multipliers      354
Lanczos vectors      238
latent root      84 see
Latent vector      84 see
Least squares      see also "Regression"
Least squares and best linear unbiased estimator      113—114
Least squares and multicollinearity      96—98 136
Least squares and solutions to a system of equations      222—228 345—346
Least squares in less than full rank models      58 228—232
Least squares in multiple regression      55—58
Least squares in one-way classification model      79—80
Least squares in ridge regression      123
Least squares in simple linear regression      50—51
Least squares inverse      196—197
Least squares inverse, computation of      203—204
Least squares with standardized explanatory variables      64—65
Least squares, generalized      141—142 245
Least squares, ordinary      26—28
Least squares, restricted      80—81 245
Least squares, weighted      65—66
Limit point      70
linear combination      33
Linear dependence      38—40
Linear equations      66—67
Linear equations and singular value decomposition      233—235
Linear equations, consistency of      210—213
Linear equations, homogeneous system of      219—221
Linear equations, least squares solutions of      222—228
Linear equations, linearly independent solutions to      217
Linear equations, solutions to      213—219
Linear equations, sparce systems of      235—241
Linear equations, sparce systems of, direct methods      235—236
Linear equations, sparce systems of, iterative methods      236—241
Linear equations, unique solution to      216
Linear independence      38—40
Linear model      27
Linear space      33
Linear transformation      60—67
LU factorization      169
Mahalanobis distance      37 63 141
Markov chain      298—300
Matrix function      327
Matrix norm      158
Matrix norm, Euclidean      158
Matrix norm, maximum column sum      158
Matrix norm, maximum row sum      158
Matrix norm, spectral      158
Matrix, block diagonal      12
Matrix, circulant      300—304
Matrix, commutation      276—283
Matrix, complex      16—18
Matrix, correlation      24
Matrix, covariance      23
Matrix, diagonal      2
Matrix, duplication      283—285
Matrix, eigenprojection      98
Matrix, elimination      285—288
Matrix, Fourier      303—304
Matrix, Hadamard      305—307
Matrix, hermitian      18
Matrix, Hessian      326
Matrix, idempotent      3 58—59 370—374
Matrix, identity      2
Matrix, indefinite      16
Matrix, irreducible      294—295
Matrix, Jacobian      327
Matrix, negative definite      16
Matrix, negative semidefinite      16
Matrix, nilpotent      127 166
Matrix, nonnegative      288
Matrix, nonnegative definite      16
Matrix, nonsingular      8
Matrix, null      2
Matrix, order of      1
Matrix, orthogonal      14—15
Matrix, partitioned      11—13
Matrix, permutation      15
Matrix, positive      288
Matrix, positive definite      15—16
Matrix, positive semidefinite      15—16
Matrix, primitive      298
Matrix, projection      52—59
Matrix, reducible      294—295
Matrix, similar      144
Matrix, skew-symmetric      4
Matrix, square root      16
Matrix, symmetric      4
Matrix, Toeplitz      304—305
Matrix, transpose      3
Matrix, triangular      2
Matrix, unitary      18 150
Matrix, Vandermonde      307—309
Maximum Likelihood Estimation      347—349
Maximum of a concave function      351
Maximum with equality constraints      353—360
Maximum, absolute      344
Maximum, conditions for local maximum      345
Maximum, local      344
Mean      19
Mean squared error      163—164
Mean vector      22
Mean vector, differences in      106—107 116—117 154
Mean vector, sample      25
Mean, sample      25
Minimum      see "Maximum"
Minor      5 13
Minor, leading principal      311
Modulus of a complex number      17
Moment generating function      20
Moments      19—20
1 2
blank
Ðåêëàìà
blank
blank
HR
@Mail.ru
       © Ýëåêòðîííàÿ áèáëèîòåêà ïîïå÷èòåëüñêîãî ñîâåòà ìåõìàòà ÌÃÓ, 2004-2024
Ýëåêòðîííàÿ áèáëèîòåêà ìåõìàòà ÌÃÓ | Valid HTML 4.01! | Valid CSS! Î ïðîåêòå