在截略資料模型下, 只有在目標變數 X 大於截略變數 T 的條件下, X 及 T 才可被觀察到. 假設截略變數之分配服從一母數族, 則可推導出目標變數之分配的半母數估計式. 此半母數估計式推導簡單且檢定力比無母數估計式好 (Wang, 1989). 本論文提出檢測截略變數之分配的卡方檢定並利用模擬方式來估計檢定之顯著性及檢定力. 在所有討論的情形下, 新檢定保有顯著性及不錯的檢定力.

關鍵字：隨機截略，半母數估計式，最大概似估計式，乘積極限估計式

Under the random truncation model, both the target variable X and the truncation variable T are observable only when T £ X. Assuming the distribution function of T follows a parametric family, a semiparametric estimator of the distribution of X is more efficient and simpler than the nonparametric estimator (Wang, 1989). In this article, we propose a chisquare test to examine this parametric assumption. The size and power of the proposed chi-square test are evaluated for small and moderate samples using Monte Carlo simulations. The proposed chi-square test is found to maintain the size and have descent powers under most of studied alternatives.

KEY WORDS: Random truncation; Semiparametric estimator; Maximum likelihood estimator; Product-limit estimator.