In this thesis, two topics in asymptotic statistics and spline functions are studied. / The first one is a study of testing the equality of Sharpe ratios. We compare two approaches to testing for the equality of many Sharpe ratios: the multivariate test of Wright et al. (2014) and Ledoit and Wolf's (2008) pairwise test. Firstly, Ledoit and Wolf's pairwise test is generalized to a multivariate one for direct comparison. We conclude by proposing a modified version that incorporates the Warp-Speed calibration method of Giacomini et al. (2013). The resulting procedure is much less computationally expensive but is comparable in its accuracy. / The second one is a study of the theoretical properties of an exponential weighting aggregated (EWA) penalized spline estimator, where the smoothing parameter is being averaged over an exponential reweighted posterior distribution. We show that the finite sample mean squared error of the EWA estimator is smaller than that of the smooth penalized spline estimator when the smoothing parameter is chosen to be a fixed value. Consistency and asymptotic normality of the EWA estimator are also developed under general situations. / 這篇論文研究了兩個關於漸近統計和樣條函數的話題。 / 其一是在假設檢驗夏普比率的相等性這個問題中的應用。我們首先比較了Wright et al.（2014）的多元檢驗方法和Ledoit & Wolf（2008）的二元檢驗方法。我們先將Ledoit & Wolf (2008)的二元檢驗法拓展到多元層面，以方便比較。最後，我們提出了採用Giacomini et al.（2013）的曲速法修改后的自助抽樣檢驗法。這種方法極大地降低了實際計算成本，同時保持了其準確性。 / 其二是對樣條估計的漸近表現的研究。我們研究了指數權重合計平滑樣條（EWA）估計，這種方法通過貝葉斯法給予平滑參數一個後驗分佈并將其加權合計。我們通過擴展一個oracle不等式驗證了EWA估計的方差比選定了一個平滑參數的一般平滑樣條估計的方差要小。此外，我們還驗證了EWA估計在一般情況下的一致性和漸近正態性。 / Huang, Wei. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 80-84). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.