The problem of n-dimensional orthogonal linear regression is a problem of finding an n-dimensional hyperplane minimising the sum of Euclidean distances between this hyperplane and a given set of m points, where m ⩾ n. This nonlinear programming problem has been re-cast in an augmented matrix...
These further assumptions, together with the linearity assumption, form a linear regression model. The next section provides an example. The normal linear regression model A popular linear regression model is the so called Normal Linear Regression Model (NLRM). In the NLRM it is assumed that: t...
For a general stationary ARMA(p,q) processuwe derive theexactform of the orthogonalizing matrixRsuch thatR′R= Σ1, where Σ =E(uu′) is the covariance matrix ofu, generalizing the known formulae forAR(p) processes. In a linear regression model with an ARMA(p,q) error process, trans...
IfAis anm×nmatrix, alinear transformationis a mapping from ℝnto ℝmdefined byy=Ax. We will deal with linear transformations throughout the remainder of this book. An excellent example is a two-dimensional linear transformation of the form ...
“Freedom of expression is the matrix, the indispensable condition, of nearly every form of freedom”(Benjamin N. Cardozo)“言论自由几乎是任何一种自由形式的母体和不可缺少的条件”(本杰明N.卡多佐)The womb.子宫Anatomy 【解剖学】 The formative cells or tissue of a fingernail, toenail, or tooth.(...
For special sets, which include an unknown matrix and correlation matrices of observation errors, such estimates were expressed through the solution of linear operator equations in a finite-dimensional space. For quasi-minimax estimates under certain assumptions, the form of the guaranteed mean squared...
Second, we propose a bi-linear matrix form, based on which multivariate discriminative analysis and logistic, Cox, and linear mixed regression are extended into their matrix-variate counterparts. Third, we systematically address the necessity, feasibility, and methodology of integrative hypothesis tests ...
This paper provides a covariance matrix estimator for the ordinary least squares coefficients of a linear time series model which is consistent even when t... DA Hsieh - 《Journal of Econometrics》 被引量: 125发表: 1983年 Tests for regression models with heteroskedasticity of unknown form Tests ...
A generic matrix-variate regression model for Y has the form $$ \boldsymbol{Y} = \boldsymbol{\beta}\boldsymbol{w}^{\top} + \boldsymbol{B} \boldsymbol{X} + \boldsymbol{U} , $$ (3) where β is the p× 1 vector consisting in the parameters related with the intercept, w is...
Using Definition 2.4, the linear system (2.14) can be rewritten in the form (2.16)[(Im⊗A)+(B⊗In)]vec(X)=vec(C). There exists a unique solution to (2.16) if and only if [(Im⊗A)+(B⊗In)] is nonsingular. However, [(Im⊗A)+(B⊗In)] is nonsingular if and only...