本文將探討在封閉性母體 (closed population) 假設下離散型重複捕取實驗中, 若自變數含有小測量誤差 (small measurement error) 時, 如何以泰勒展式近似原始的估計方程式與母體估計量來進行分析, 進而提供一個方便、 有效率且無需許多假設的估計方法。 最後我們以模擬方法考量自變數與隨機誤差在不同分配之下各種估計方法的表現, 並計算不同估計方法的平均估計值、 相對偏差 (RB) 與估計值的樣本標準差、 平均估計標準差、 樣本均方根誤差 (RMSE) 與 95% 信賴區間涵蓋率 (CP), 最後並對所得的結果加以討論。 In a regression analysis, it may happen that variables are not measured precisely. When the covariates are measured with measurement errors, the estimation in regression parameters will be biased in usual. However, for the capture-recapture experiments, the investigations into the effect of measurement errors have been very limited.
Besides the approaches of regression calibration and conditional score that proposed by Hwang and Huang (2003, 2005), the present paper disscusses an approximate estimation through Taylor expansion for the discrete time capture-recapture experiment. As a result, we find that the small measurement error approximation is a convenient and efficient way for estimaing both in regression parameters and in the population size. Simulation results are also provided for different distributions of measurement error and covariate.
