本計畫是前國科會計畫: 條件相關性度量及條件獨立檢定 (95-2119-M-004-001, 2006.10.01-2007.07.31) 的後續研究. 在前計畫中根據所建立的條件相關性度量提出了 一個檢定統計量，用來檢定變數X and Y 在給定變數Z=z 時是否為條件獨立。所提出 的檢定統計量牽涉到對X 和Y 的函數空間做近似，這部分透過一些函數基底去處理。 如果要求所得到的檢定是consistent, 則基底個數必須隨樣本數n 增加而增加。然而在 這種情況下檢定統計量的漸進分布還不知道。本計畫的目的就是推導出檢定統計量的漸 進分布。預計會用到分布為 Wishart distribution 的隨機矩陣最大特徵值的漸進分布以 及IID 隨機向量和的近似理論。 This project is a follow-up of a former NSC project on measures of conditional association and testing conditional independence (95-2119-M-004-001). In the former project, a test statistic based on a measure of conditional association is given for testing the hypothesis that two vectors X and Y are independent given a third vector Z=z. Such a statistic is constructed by approximating some function spaces using finite dimensional function spaces spanned by some basis functions. For the test based on the proposed statistic to be consistent, it is necessary that the dimensions of the approximating function spaces tend to infinity as the sample size n tends to infinity. However, the asymptotic distribution of the test statistic in this case is unknown. In this project, it is proposed to derive the asymptotic distribution of the test statistic using results on the limiting distribution of the maximum eigenvalue of a matrix following a Wishart distribution and approximation theory of partial sums of IID random vectors.