Definitions for cross-covariance
cross-covari·ance

WikipediaRate this definition:0.0 / 0 votes

1. Cross-covariance

   In probability and statistics, given two stochastic processes { X t } {\displaystyle \left\{X_{t}\right\}} and { Y t } {\displaystyle \left\{Y_{t}\right\}} , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation E {\displaystyle \operatorname {E} } ; for the expectation operator, if the processes have the mean functions μ X ( t ) = E ⁡ [ X t ] {\displaystyle \mu _{X}(t)=\operatorname {\operatorname {E} } [X_{t}]} and μ Y ( t ) = E ⁡ [ Y t ] {\displaystyle \mu _{Y}(t)=\operatorname {E} [Y_{t}]} , then the cross-covariance is given by K X Y ⁡ ( t 1 , t 2 ) = cov ⁡ ( X t 1 , Y t 2 ) = E ⁡ [ ( X t 1 − μ X ( t 1 ) ) ( Y t 2 − μ Y ( t 2 ) ) ] = E ⁡ [ X t 1 Y t 2 ] − μ X ( t 1 ) μ Y ( t 2 ) . {\displaystyle \operatorname {K} _{XY}(t_{1},t_{2})=\operatorname {cov} (X_{t_{1}},Y_{t_{2}})=\operatorname {E} [(X_{t_{1}}-\mu _{X}(t_{1}))(Y_{t_{2}}-\mu _{Y}(t_{2}))]=\operatorname {E} [X_{t_{1}}Y_{t_{2}}]-\mu _{X}(t_{1})\mu _{Y}(t_{2}).\,} Cross-covariance is related to the more commonly used cross-correlation of the processes in question. In the case of two random vectors X = ( X 1 , X 2 , … , X p ) T {\displaystyle \mathbf {X} =(X_{1},X_{2},\ldots ,X_{p})^{\rm {T}}} and Y = ( Y 1 , Y 2 , … , Y q ) T {\displaystyle \mathbf {Y} =(Y_{1},Y_{2},\ldots ,Y_{q})^{\rm {T}}} , the cross-covariance would be a p × q {\displaystyle p\times q} matrix K X Y {\displaystyle \operatorname {K} _{XY}} (often denoted cov ⁡ ( X , Y ) {\displaystyle \operatorname {cov} (X,Y)} ) with entries K X Y ⁡ ( j , k ) = cov ⁡ ( X j , Y k ) . {\displaystyle \operatorname {K} _{XY}(j,k)=\operatorname {cov} (X_{j},Y_{k}).\,} Thus the term cross-covariance is used in order to distinguish this concept from the covariance of a random vector X {\displaystyle \mathbf {X} } , which is understood to be the matrix of covariances between the scalar components of X {\displaystyle \mathbf {X} } itself. In signal processing, the cross-covariance is often called cross-correlation and is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time between the signals, is sometimes called the sliding dot product, and has applications in pattern recognition and cryptanalysis.

How to pronounce cross-covariance?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say cross-covariance in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of cross-covariance in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of cross-covariance in Pythagorean Numerology is: 3

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Cross-Covariance