隨著科技不斷的進步，人們需要處理的資料量也不斷地增加。在巨量資料的分析上，維度縮減將有助於增進效率。本篇論文主要介紹切片平均變異數估計維度縮減方法，並將此法應用於整體相關性檢定問題上。我們考慮切片平均變異數估計法中的邊際維度檢定，並將利用排列重抽法建構檢定統計量的虛無分配，藉此計算排列顯著值來獲得統計推論。此整體相關性檢定可用在基因組分析問題上，以驗證特定基因組與外顯特徵變數間的相關程度。最後我們將模擬本檢定的型一誤差率和檢定力，並與前人提出的方法做比較。

在現今生物醫學領域中，一重要課題為透過基因實驗所獲得的量化資料，來研究與分析基因與外顯表型變數(phenotype)的相關性。已知多數已發展的方法皆屬於單基因分析法，無法適當的考慮基因之間的相關性。本研究主要針對基因組分析(gene set analysis)問題，提出統計檢定方法來驗證特定基因組的顯著性。為了能盡其所能的捕捉整體基因組與外顯表型變數的關係，我們結合了傳統的檢定方法與分類方法，提出以隨機森林分類方法(Random Forests)的測試組分類誤差值(test error)作為檢定統計量(test statistic)，並以其排列顯著值(permutation-based p-value)來獲得統計結論。我們透過模擬研究將本研究方法和其他七種基因組分析方法做比較，可發現本方法在型一誤差率(type I error rate)和檢定力(power)上皆有優異表現。最後，我們運用本方法在數個實際基因資料組的分析上，並深入探討所獲得結果。 / Nowadays microarray data analysis has become an important issue in biomedical research. One major goal is to explore the relationship between gene expressions and some specific phenotypes. So far in literatures many developed methods are single gene-based methods, which use solely the information of individual genes and cannot appropriately take into account the relationship among genes. This research focuses on the gene set analysis, which carries out the statistical test for the significance of a set of genes to a phenotype. In order to capture the relationship between a gene set and the phenotype, we propose the use of performance of a complex classifier in the statistical test: The test error rate of a Random Forests classification is adopted as the test statistic, and the statistical conclusion is drawn according to its permutation-based p-value. We compare our test with other seven existing gene set analyses through simulation studies. It’s found that our method has leading performance in terms of having a controlled type I error rate and a high power. Finally, this method is applied in several real examples and brief discussions on the results are provided.