Isotalo J., Puntanen S — Formulas Useful for Linear Regression Analysis and Related Matrix Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Isotalo J., Puntanen S — Formulas Useful for Linear Regression Analysis and Related Matrix Theory

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Название: Formulas Useful for Linear Regression Analysis and Related Matrix Theory

Авторы: Isotalo J., Puntanen S

Аннотация:

This booklet comprises some formulas that we have found useful for linear regression analysis and related matrix theory. This is a kind of survival kit for teaching and research of this area.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 2005

Количество страниц: 85

Добавлена в каталог: 10.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Added variable plot      18
Algebraic multiplicity      64
anova      29
Antieigenvalue      48
AR(l)-structure      50 52
Banachiewicz — Schur form      59
Best linear predictor      23
Best linear predictor, BLP(z | Az)      24
Best linear unbiased estimator, $BLUE(K\beta)$       41
Best linear unbiased estimator, $BLUE(X\beta)$       41
Best linear unbiased estimator, restricted BLUE      30
Best linear unbiased predictor      52
Bias      22
Block diagonalization      24
Bloomfield — Watson efficiency      49
Canonical correlation      48 67
Cauchy — Schwarz inequality      76
Centered and scaled $X_{y}$       3
Centered model      9
Centered, $X_{0}$       2
Centered, $X_{y}$       2
Centered, y      2
Centering matrix C      2
Cholesky decomposition      70
Coefficient of determination, $R^{2}$       15
Collinearity      33
Column space, definition      4
Column space, orthocomplement      4
Condition indexes      33
Condition number      33
Confidence interval for $E(y_{*})$       13
Confidence interval for $\beta_{i}$       12
Confidence interval, Working-Hotelling confidence band      13
Confidence region for $\beta_{(2)}$       27
Confidence region for $\beta_{2}$       26
Consistency of linear model      42
Cook, R. Dennis      24
Cook’s distance      32
Correlation $cor(e_{i}, e_{j})$       7
Correlation $cor(\widehat{\beta}_{1}, \widehat{\beta}_{2})$       12
Correlation $kor(x_{i}, x_{j})$       3
Correlation $R=kor{y, \widehat{y})$       8
Correlation as a cosine      3
Correlation matrix $cov(e_{y\cdot x},x)$       23
Correlation matrix $kor(X_{0} : y) = R$       3
Correlation matrix $kor(X_{0}) = R_{1}$       3
Correlation matrix       4
Correlation matrix cor(x)      5
Correlation matrix, intraclass      56
Correlation, between dichotomous variables      4
Correlation, canonical      48
Correlation, partial correlation      17
Courant — Fischer      65
Covariance       25
Covariance adjustment principle      23
Covariance matrix of the prediction error      23 24 69
Covariance matrix, $cov(e_{y\cdot x})$       23
Covariance matrix, $cov(X\widetilde{\beta})$       42
Covariance matrix, $cov(\widehat{\beta_{2}})$       11
Covariance matrix, $cov(\widehat{\beta})$       10
Covariance matrix, $kov(X_{0}) = S_{1}$       3
Covariance matrix, $kov(X_{y}) = S$       3
Covariance matrix, $\widehat{cov}(\widehat{\beta})$       12
Covariance matrix, cov(x)      4
Covariance matrix, cov(x, y)      5
Covariance matrix, cov[z — BLP(z | Az)]      24
Covariance matrix, intraclass      57
Covariance matrix, partial covariance      20
Cronbach’s alpha      78
Das Gupta, Somesh      25
Data matrix, $X_{0}$       1
Data matrix, $X_{y} = (X_{0} : y)$       2
Data matrix, best rank-k approximation      69
Decomposition, recursive dec. of $1-R^{2}(\mathcal{M}_{1 2})$       16
Decomposition, recursive dec. of $1-\rho^{2}_{y\cdot 12...p'}$       24
Disjointness, $\ell(A)\cap\ell(B)={0}$       75
Durbin — Watson test statistic      51
Eckart — Young Theorem      66 68
Eigenspace      64
Eigenvalue decomposition      67
Eigenvalues, $\{nzch(AB)\} = \{(nzch(BA)\}$       66
Equality between OLSE and BLUE      45
Estimability of $K'\beta$       30
Estimability of $K_{2}\beta_{2}$       31
Estimability of $X_{2}\beta_{2}$       92 31
Extended (mean-shift) model      31
Fitted values      6
Frisch — Waugh — Lovell Theorem      9 18
Frobenius inequality      74
Full rank decomposition      69
Generalized variance      4 5
Geometric multiplicity      64
Hat matrix H      5
Henderson’s mixed model equations      53
Hotelling’s $T^{2}$       22
Inequality, Cauchy — Schwarz      76
Inequality, Frobenius      74
Inequality, Kantorovich      76
Inequality, Samuelson’s      78
Inequality, Sylvester’s      74
Inequality, Wielandt      76
Inertia      72
intercept      8
Interlacing theorem      66
Intraclass, correlation structure      46 56
Intraclass, covariance structure      57
Invariance of $\ell(AB — C)$       58
Invariance of $\ell(X'W — X)$       40
Invariance of AB — C      58
Invariance of r(AB — C)      58
Invariance of r(X'W — X)      40
Invariance of X'W — X      40
Jordan block      70
Jordan decomposition      70
Kantorovich Inequality      76
Least-squares g-inverse      60
Left singular vector      68
Lehmann — Scheffe theorem      52
Leverage $h_{ii}$       33

Likelihood function      22
Linear Bayes estimator      14
Linear model, definition      1
Linear zero function      41
Linearly complete      51
Linearly minimal sufficient      51
Linearly sufficient      51
Mahalanobis distance, $MHLN^{2}(u, \mu)$       4 21
Mahalanobis distance, $MHLN^{2}(x_{(0*)}, \overline{\overline{x}})$       12
Marquardt estimator      13
Matrix angle      48
Matrix of corrected sums of squares $X'_{y}CX_{y}$       2
Matrix, $A^{\bot}$       4 74
Matrix, commutation      79
Matrix, shorted      73
Matrix, triangular factorization      25 70
Maximising, cor(y, b'x)      24
Maximising, var(b'z)      69
Mean squared error      22
Minimising, cov(y — Fx)      23
Minimising, orthogonal distances      69
Minimising, var(y - b'x)      24
Minimum norm g-inverse      60
Minor of A      53
Minus partial ordering      72
Mixed model      53
Model matrix X      1
Multiple correlation in $\mathcal{M}_{12\cdot 1}$       16
Multiple correlation in no-intercept model      16
Multiple correlation, $R = kor(y, \widehat{y})$       8
Multiple correlation, population      24
Multiple correlation, squared $R^{2}$       15
Mustonen’s measure of multivariate dispersion      24
Normal distribution, conditional      19
Normal distribution, conditional mean      20
Normal distribution, conditional variance      20
Normal distribution, definition      19
Normal equation      7
Normal equation, general solution      7
Null space      4
Observation space      2
Observation vector      2
Ordinary least squares estimator, $OLSE(X\beta)$       6
Ordinary least squares estimator, $OLSE(\beta)$       8
Ordinary least squares estimator, fitted values      6
Ordinary least squares estimator, restricted OLSE      27
Orthogonal rotation      70
Overall-F value      28
Pandora Box      41 43
Partial correlation, $pkor(X_{1} | X_{2})$       17
Partial correlation, $r_{xy\cdot z}$       17
Partial covariance $cov(z_{2} | \underline{z}_{1})$       20
Poincare separation theorem      65
Polar decomposition      70
Predicted value $\widehat{y}_{*}$       12
Prediction error      12
Prediction error, y - BLP(y | x)      19 23 15 25
Prediction interval for $y_{*}$       13
Principal component analysis, definition      68
Principal component analysis, matrix approximation      69
Principal component analysis, predictive approach      69
Principal component analysis, sample principal components      69
Principal components estimator      13
Principal minor of A      53
Projector, $P_{A | B}$       36
Projector, $P_{X;V^{-1}}$       36
Projector, C      2
Projector, H      5
Projector, J      2
Projector, M      6
Projector, Schur complement, $P_{22\cdot 1}$       62
QR-decomposition      70
Rank cancellation rule      73
Rank-subtractivity partial ordering      72
Reduced model $\mathcal{M}_{12\cdot 1}$       9
Regression coefficients      8
Regression coefficients, old ones do not change      9
Regression coefficients, standardized      10
Regression function      20
Regression mean square, MSR      15
Residual mean square, MSE      15
Residual of BLUE      39 44
Residual of OLSE      7 31
Residual sum of squares, SSE      14
Residual, after elimination of $X_{1}$       15
Residual, externally Studentized      31
Residual, internally Studentized      31
Residual, predicted residual      32
Residual, scaled      31
Ridge estimator      13
Right singular vector      68
Samuelson’s inequality      78
Schur complement      54
Schur’s Triangularization theorem      70
Shorted matrix      73
Shrinkage estimator      13
Shrinkage estimator, Farebrother      14
Shrinkage estimator, Ohtani      14
Shrinkage estimator, Stein      14
Simultaneous diagonalization      66
Singular value decomposition      67
Square root of matrix      70
Standard error of $\widehat{\beta}_{i}$       12
Sum of products $SP_{xy} = t_{xy}$       3
Sum of squares due to regression, SSR      14
Sum of squares, $SS_{y} = t_{yy}$       3
Sum of squares, change in SSE      15 26 27
Sum of squares, change in SSE(V)      30
Sum of squares, predicted residual      32
Sum of squares, SSE      14
Sum of squares, SSE under $\mathcal{M}_{12\cdot 1}$       16
Sum of squares, SSR      14
Sum of squares, SST      14
Sum of squares, weighted SSE      29 39 44
Sylvester’s inequality      74
Total sum of squares, SST      14
Triangular factorization      25
Triangular matrix      70
Unbiased estimator of $\sigma^{2}$       2 15 29 30 44
Working — Hotelling confidence band      13

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