許多重要的統計方法建立在常態性假設成立的基礎之上。因此，各式各樣的常態性檢定常用來檢驗這些統計方法，避免違反常態性假設。本論文先重新審視一些常用的常態性檢定方法，再提出新的檢定方法。如同訊息矩陣檢定給我們的啟示，本論文提出的檢定統計量是由兩個變異數矩陣之行列式組成的比例式。分子部分是變異數三明治估計式之行列式，常用來建立估計方程式，而分母部分是費雪訊息矩陣的反矩陣之行列式。當樣本數大，且滿足常態性假設的時候，本論文提出的檢定統計量會機率收斂至1。此外，本檢定統計量，也是特定的經驗貝式模型中的貝式因子。再者，本檢定統計量，也可由超值峰態係數以及偏態係數平方值的加權總合所表達。在樣本數大，虛無假設之下，本檢定統計量可用常態分配良好的近似。

本研究提出的檢定方法，經過了模擬與研究在不同樣本數之下的檢定力表現後，發現在樣本數達100之後，它能夠有良好的表現，不遜於一些目前常用的常態性檢定方法。本研究也用此檢定方法，去檢驗體脂肪百分比預測模型的常態性假設和股票對數收益率之布朗運動模型假設。並整理出本檢定方法與目前常用的常態性檢定方法的檢定結果。

Many fundamental statistical methods root in normal assumption. Therefore, a variety of normality tests are frequently applied to these methods to prevent normal assumption violation. In this thesis, we first review popular normality tests and then propose a new normality test. The test statistic, as motivated by information matrix test, is the ratio of determinants of two variance matrices. The numerator is the determinant of the sandwich variance formula often used in estimating equation approaches whereas the denominator is the determinant of the inverse of Fisher's information matrix. When the sample size is large and the normal assumption is true, the test statistic converges in probability to 1. Moreover, the test statistic is also the Bayes factor of a particular empirical Bayesian model. Furthermore, the test statistic can be expressed as the weighted sum of the excess kurtosis and the skewness square. Under the null hypothesis and for large sample, the test statistic can be well-approximated by a normal distribution.

We simulated and studied the size and power of the proposed test and found that it is compatible with some popularly used normality tests when sample size is as large as 100. We also applied the proposed test to examine the normal assumption on the body fat percentage prediction and to examine the Brownian motion assumption on the log-returns of stock prices. And we showed the consequences of the proposed test and popularly used normality tests.

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