- 學位論文
分類變數的統計推論與其截尾平均數的應用
Statistical Inferences with Categorized Variables and Its Application to a Trimmed Mean
摘要
對於分類連續型變數，學界已付出相當多的努力在爭論此某些不佳的統計推論特性，但此一方法在解釋分析結果上有誘人的方便性，我們無法阻擋此方法在流行病學研究領域的普及。為了修正這個大多數人都在使用但其又不可信賴的統計方法，我們建立有母數及無母數估計量，並研究其統計上的理論，且我們證明了有母數樣本平均數的理論其說明為何這個傳統的統計方法的效果不彰。在(非分類的)單變數母體平均的無母數估計量，我們證明分類對於提高有母數估計量的效率能產生輔助資訊，這證明了統計界完全不知道分類方法的統計特性以及額外變數利用分類的統計推論增加的母體資訊，此方法在文獻上應該受到更多的注意。
並列摘要
Considerable energy has been devoted to the arguments of possible undesired statistical inference properties resulted from categorization of continuous variables that does not stop its popularity in association research of epidemiology for its appealing of convenience in presentation and interpretation of analyzed results. For correction of popularly used untrustworthy statistical methods, we initiate a theoretical study of statistical effect of categorization with parametric and nonparametric estimations for unknown means of categorized variables. We show that the parametric sample mean is very effcient that explains undesired statistical property of classical statistical methods. In nonparametric estimation of the population mean of a (noncategorized) variable, we prove that categorization creates auxiliary information to improve the effciency of parameter estimation. This shows that the statistical society is far from knowing the statistical properties of categorization and the supplementary population information of an extra variable created by categorization for statistical inferences deserves to receive more attention in literature.