Matrix Differential Calculus with Applications

[1]  H. Neudecker,et al.  Exact Linear Restrictions on Parameters in the General Linear Model with a Singular Covariance Matrix , 1977 .

[2]  C. Dubbelman,et al.  A new class of disturbance estimators in the general linear model , 1972 .

[3]  Edward E. Leamer,et al.  Specification Searches: Ad Hoc Inference with Nonexperimental Data , 1980 .

[4]  Letter to the editor on some frequently occurring errors in the economic literature concerning problems of maxima and minima , 1974 .

[5]  J. Magnus On Differentiating Eigenvalues and Eigenvectors , 1985, Econometric Theory.

[6]  P. S. Dwyer,et al.  Symbolic Matrix Derivatives , 1948 .

[7]  N. Urquhart Generalized Inverse Matrices (with Applications to Statistics) , 1973 .

[8]  K. Fan On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations: II. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[10]  J. Magnus,et al.  The Commutation Matrix: Some Properties and Applications , 1979 .

[11]  Ken Binmore,et al.  Mathematical analysis : a straightforward approach , 1982 .

[12]  M. Marcus,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[13]  Charles E. McCulloch,et al.  Symmetric Matrix Derivatives with Applications , 1982 .

[14]  R. J. Sherin,et al.  A matrix formulation of Kaiser's varimax criterion , 1966, Psychometrika.

[15]  W. Rheinboldt,et al.  On a generalization of an inequality of L. V. Kantorovich , 1959 .

[16]  J. Magnus,et al.  Symmetry, 0-1 Matrices and Jacobians: A Review , 1986, Econometric Theory.

[17]  P. Lancaster On eigenvalues of matrices dependent on a parameter , 1964 .

[18]  H. Theil Principles of econometrics , 1971 .

[19]  Jan R. Magnus,et al.  The Elimination Matrix: Some Lemmas and Applications , 1980, SIAM J. Algebraic Discret. Methods.

[20]  Chi Song Wong On the use of differentials in statistics , 1985 .

[21]  F. Downton,et al.  Introduction to Mathematical Statistics , 1959 .

[22]  F. Fisher,et al.  The Identification Problem in Econometrics. , 1967 .

[23]  G. Stewart On the Continuity of the Generalized Inverse , 1969 .

[24]  G. Debreu Definite and Semidefinite Quadratic Forms , 1952 .

[25]  Heinz Neudecker,et al.  A matrix trace inequality , 1992 .

[26]  Patrick L. Odell,et al.  Generalized Inverse Matrices , 1971 .

[27]  Wolfgang Polasek,et al.  The Hadamard Product and Some of its Applications in Statistics , 1995 .

[28]  Calyampudi R. Rao Estimation and tests of significance in factor analysis , 1955 .

[29]  H. Neudecker,et al.  The heteroskedastic linear regression model and the Hadamard product a note , 1995 .

[30]  Best quadratic unbiased estimation of the variance matrix in normal regression , 1980 .

[31]  C. Radhakrishna Rao,et al.  Unified theory of linear estimation , 1971 .

[32]  R. H. Norden A Survey of Maximum Likelihood Estimation , 1972 .

[33]  Jerry G. Thursby,et al.  Econometric Applications of Maximum Likelihood Methods. , 1988 .

[34]  R. Penrose On best approximate solutions of linear matrix equations , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[35]  A new proof of the Milliken-Akdeniz theorem , 1989 .

[36]  D.S.G. Pollock,et al.  Tensor products and matrix differential calculus , 1985 .

[37]  L. Mirsky,et al.  An introduction to linear algebra , 1957, Mathematical Gazette.

[38]  J. Rolle Best Nonnegative Invariant Partially Orthogonal Quadratic Estimation in Normal Regression , 1994 .

[39]  A. Hoffman,et al.  Some metric inequalities in the space of matrices , 1955 .

[40]  W. Fleming Functions of Several Variables , 1965 .

[41]  J. Rolle Optimization of functions of matrices with an application in statistics , 1996 .

[42]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[43]  Albert Madansky,et al.  Foundations of Econometrics , 1975 .

[44]  George Zyskind,et al.  On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure , 1969 .

[45]  Leigh Tesfatsion,et al.  Variational equations for the eigenvalues and eigenvectors of nonsymmetric matrices , 1981 .

[46]  P. Schonemann,et al.  On the Formal Differentiation of Traces and Determinants. , 1985, Multivariate behavioral research.

[47]  Tom Wansbeek,et al.  Some results on commutation matrices, with statistical applications , 1983 .

[48]  Calyampudi R. Rao,et al.  Linear statistical inference and its applications , 1965 .

[49]  J. Sargan,et al.  On the theory and application of the general linear model , 1970 .

[50]  T. Rothenberg,et al.  Efficient Estimation of Simultaneous Equation Systems , 1964 .

[51]  H. Hotelling Analysis of a complex of statistical variables into principal components. , 1933 .

[52]  H. Theil The Analysis of Disturbances in Regression Analysis , 1965 .

[53]  W. Rudin Principles of mathematical analysis , 1964 .

[54]  R. Kalaba,et al.  A New Differential Equation Method for Finding the Perron Root of a Positive Matrix , 1980 .

[55]  L. Kantorovich,et al.  Functional analysis and applied mathematics , 1963 .

[56]  M. H. Moore A Convex Matrix Function , 1973 .

[57]  John S. Chipman,et al.  On Least Squares with Insufficient Observations , 1964 .

[58]  John L. Lastovicka,et al.  The extension of component analysis to four-mode matrices , 1981 .

[59]  G. Styan Hadamard products and multivariate statistical analysis , 1973 .

[60]  A. Barten Maximum likelihood estimation of a complete system of demand equations , 1969 .

[61]  Chi Song Wong,et al.  Minima and maxima in multivariate analysis , 1980 .

[62]  E. Fischer Über quadratische Formen mit reellen Koeffizienten , 1905 .

[63]  K. Fan On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[64]  H. Neudecker,et al.  Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices , 1993 .

[65]  Tony Lancaster,et al.  THE COVARIANCE MATRIX OF THE INFORMATION MATRIX TEST , 1984 .

[66]  Kunio Tanabe,et al.  An exact Cholesky decomposition and the generalized inverse of the variance-covariance matrix of the multinomial distribution, with applications , 1992 .

[67]  Shuangzhe Liu Contributions to matrix calculus and applications in econometrics , 1996 .

[68]  Ou Ziqiang,et al.  Estimation of variance and covariance components , 1989 .

[69]  Recent Advances in Statistical Applications of Commutation Matrices , 1985 .

[70]  J. Edward Jackson The Algebra of Econometrics , 1980 .

[71]  W. E. Roth On direct product matrices , 1934 .

[72]  R. Muirhead Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[73]  A. Zellner An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[74]  H. Bozdogan On the information-based measure of covariance complexity and its application to the evaluation of multivariate linear models , 1990 .

[75]  Multivariate linear normal models : with special references to the growth curve model , 1985 .

[76]  J. Dieudonne Foundations of Modern Analysis , 1969 .

[77]  H. Neudecker,et al.  On matrix procedures for optimizing differentiable scalar functions of matrices , 1967 .

[78]  H. Neudecker De BLUF‐schatter: een rechtstreekse afleiding , 1973 .

[79]  Pietro Balestra Best quadratic unbiased estimators of the variance-covariance matrix in normal regression , 1973 .

[80]  H. Neudecker Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products , 1969 .

[81]  A. C. Aitken,et al.  Determinants and matrices , 1940 .

[82]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[83]  C. R. Rao,et al.  Generalized Inverse of Matrices and its Applications , 1972 .

[84]  M. Wickens,et al.  A simple derivation of the limited information maximum likelihood estimator , 1982 .

[85]  J. Koerts,et al.  New Estimators of Disturbances in Regression Analysis , 1971 .

[86]  P. S. Dwyer Some Applications of Matrix Derivatives in Multivariate Analysis , 1967 .

[87]  A DERIVATION OF THE HESSIAN OF THE (CONCENTRATED) LIKELIHOOD FUNCTION OF THE FACTOR MODEL EMPLOYING THE SCHUR PRODUCT , 1975 .

[88]  Richard J. Smith Wald tests for the independence of stochastic variables and disturbance of a single linear stochastic simultaneous equation , 1985 .

[89]  G. Milliken,et al.  A theorem on the difference of the generalized inverses of two nonnegative matrices , 1977 .

[90]  G. H. Golub,et al.  Differentiation of Pseudoinverses, Separable Nonlinear Least Square Problems and Other Tales , 1976 .

[91]  J. Magnus,et al.  Matrix differential calculus with applications to simple, Hadamard, and Kronecker products. , 1985 .

[92]  Hamparsum Bozdogan,et al.  Mixture-Model Cluster Analysis Using Model Selection Criteria and a New Informational Measure of Complexity , 1994 .

[93]  H. Neudecker Bounds for the Bias of the Least Squares Estimator of s2 in the Case of a First-order Autoregressive Process (Positive Autocorrelation) , 1977 .

[94]  P. Bentler,et al.  Matrix derivatives with chain rule and rules for simple, Hadamard, and Kronecker products , 1978 .

[95]  R.D.H. Heijmans,et al.  Asymptotic Normmality of Maximum Likelihood Estimators Obtained from Normally Distributed but Dependent Observations , 1986, Econometric Theory.

[96]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[97]  Jan R. Magnus,et al.  On the fundamental bordered matrix of linear estimation , 1990 .

[98]  S. R. Searle,et al.  Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics , 1979 .

[99]  H. Neudecker Bounds for the Bias of the LS Estimator of [sigma][superscript]2 in the Case of a First-Order (Positive) Autoregressive Process When the Regression Contains a Constant Term , 1978 .

[100]  Jan R. Magnus,et al.  A note on instrumental variables and maximum likelihood estimation procedures , 1986 .

[101]  T. A. A. Broadbent,et al.  Elements of Linear Spaces , 1963 .

[102]  E. C. Macrae Matrix Derivatives with an Application to an Adaptive Linear Decision Problem , 1974 .

[103]  T. Apostol Mathematical Analysis , 1957 .

[104]  H. Kaiser Computer Program for Varimax Rotation in Factor Analysis , 1959 .

[105]  Ingram Olkin An inequality for a sum of forms , 1983 .

[106]  H. Neudecker,et al.  Asymptotics of Pearson-Hotelling principal-component vectors of sample variance and correlation matrices. , 1997 .

[107]  David R. Brillinger,et al.  Statistical Methods of Econometrics. , 1967 .

[108]  H. Kaiser The varimax criterion for analytic rotation in factor analysis , 1958 .

[109]  The best quadratic estimator of the residual variance in regression analysis , 1961 .

[110]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[111]  Paul S. Dwyer,et al.  Multivariate Maxima and Minima with Matrix Derivatives , 1969 .

[112]  R. H. Norden A Survey of Maximum Likelihood Estimation: Part 2 , 1973 .

[113]  Arthur Albert,et al.  THE GAUSS-MARKOV THEOREM FOR REGRESSION MODELS WITH POSSIBLY SINGULAR COVARIANCES* , 1973 .

[114]  H. Neudecker A comment on “minimization of functions of a positive simidefinite matrix A subject to AX = 0” , 1980 .

[115]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[116]  On the dispersion matrix of a matrix quadratic form connected with the noncentral Wishart distribution , 1985 .

[117]  Leigh Tesfatsion,et al.  Individual tracking of an eigenvalue and eigenvector of a parameterized matrix , 1981 .

[118]  H. Wolkowicz,et al.  Bounds for eigenvalues using traces , 1980 .

[119]  M. R. B. Clarke,et al.  A RAPIDLY CONVERGENT METHOD FOR MAXIMUM-LIKELIHOOD FACTOR ANALYSIS , 1970 .

[120]  A Note on Quadratic Forms Positive Definite under Linear Constraints , 1968 .

[121]  T. Andô,et al.  On the arithmetic-geometric-harmonic-mean inequalities for positive definite matrices , 1983 .

[122]  D. G. Nel On matrix differentiation in statistics , 1980 .

[123]  Shein-Chung Chow,et al.  Advanced Linear Models. , 1995 .

[124]  C. Rao Markoff's theorem with linear restrictions on parameters , 1945 .

[125]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[126]  Margaret E. Baron,et al.  The origins of the infinitesimal calculus , 1969 .

[127]  P. Schonfeld Best Linear Minimum Bias Estimation in Linear Regression , 1971 .

[128]  M. Browne Generalized Least Squares Estimators in the Analysis of Covariance Structures. , 1973 .

[129]  N. Sugiura,et al.  Derivatives of the characteristic root of a synmetric or a hermitian matrix with two applications in multivariate analysis , 1973 .

[130]  R. W. Farebrother,et al.  Necessary and sufficient conditions for a quadratic form to be positive whenever a set of homogeneous linear constraints is satisfied , 1977 .

[131]  Heinz Neudecker,et al.  On the matrix formulation of Kaiser's varimax criterion , 1981 .

[132]  C. C. Macduffee,et al.  The Theory of Matrices , 1933 .

[133]  T. Andô Concavity of certain maps on positive definite matrices and applications to Hadamard products , 1979 .

[134]  Chi Song Wong Matrix derivatives and its applications in statistics , 1980 .

[135]  Hans Hahn The fundamental theorems of the differential calculus , 1913 .

[136]  D. F. Morrison,et al.  Multivariate Statistical Methods , 1968 .