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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cross-covariance ： ウィキペディア英語版 Cross-covariance In probability and statistics, given two stochastic processes $X=(X\_t)$ and $Y=(Y\_t)$, the cross-covariance is a function that gives the covariance of the one process with the other at pairs of time points. With the usual notation ''E''  for the expectation operator, if the processes have the mean functions $\backslash mu\_t\; =\; E()$ and $\backslash nu\_t\; =\; E()$, then the cross-covariance is given by :$C\_(t,s)\; =\; cov(X\_t,\; Y\_s)\; =\; E(-\; \backslash mu\_t)(Y\_s\; -\; \backslash nu\_s))\; =\; E(Y\_s)\; -\; \backslash mu\_t\; \backslash nu\_s.\backslash ,$ Cross-covariance is related to the more commonly used cross-correlation of the processes in question. In the case of two random vectors $X=(X\_1,\; X\_2,\; ...\; ,\; X\_n)$ and $Y=(Y\_1,\; Y\_2,\; ...\; ,\; Y\_n)$, the ''cross-covariance'' would be a square ''n'' by ''n'' matrix $C\_$ with entries $C\_(j,k)\; =\; cov(X\_j,\; Y\_k).\backslash ,$ Thus the term ''cross-covariance'' is used in order to distinguish this concept from the "covariance" of a random vector ''X'', which is understood to be the matrix of covariances between the scalar components of ''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. (詳細はrandom vectors ''X'' and ''Y'', each containing random elements whose expected value and variance exist, the cross-covariance matrix of ''X'' and ''Y'' is defined by :$\backslash operatorname(X,Y)=\backslash operatorname(),$ where ''μX'' and ''μY'' are vectors containing the expected values of ''X'' and ''Y''. The vectors ''X'' and ''Y'' need not have the same dimension, and either might be a scalar value. Any element of the cross-covariance matrix is itself a "cross-covariance". 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cross-covariance」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.