Search results
Results From The WOW.Com Content Network
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. The term error-correction relates to the fact that last-period's deviation from a long-run equilibrium, the error, influences its short-run dynamics. Thus ECMs directly estimate the speed at which a dependent ...
A vector's components change scale inversely to changes in scale to the reference axes, and consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including rotation and ...
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
=, where is a lower triangular matrix obtained by a Cholesky decomposition of such that = ′, where is the covariance matrix of the errors Φ i = J A i J ′ , {\displaystyle \Phi _{i}=JA^{i}J',} where J = [ I k 0 … 0 ] , {\displaystyle J={\begin{bmatrix}\mathbf {I} _{k}&0&\dots &0\end{bmatrix}},} so that J {\displaystyle J} is a k ...
When the two random vectors are the same, the cross-covariance matrix is referred to as covariance matrix. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable.
In statistics, a covariate represents a source of variation that has not been controlled in the experiment and is believed to affect the dependent variable. [8] The aim of such techniques as ANCOVA is to remove the effects of such uncontrolled variation, in order to increase statistical power and to ensure an accurate measurement of the true relationship between independent and dependent ...
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices.If we have two vectors X = (X 1, ..., X n) and Y = (Y 1, ..., Y m) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y that have a maximum ...