具有異質性測量誤差的重複捕取實驗之估計

Estimations in capture-recapture experiments with heterogeneous measurement errors

籃揚凱(Yang-Kai Lan)

指導教授 ： 黃逸輝

淡江大學/理學院/數學學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00826

摘要

在本文中,我們探討離散型重複捕取實驗的自變數有異質性測量誤差的估計方法。在重複捕取實驗中至少有兩種情況應考慮異質性測量誤差。一個是測量誤差大小可能與真實自變數大小有關;另一個是個體被重複測量的次數會因捕取次數不同而造成測量誤差大小不同。
因此異質性誤差的假設,相較於大部分文獻所採用的同質性誤差的假設,顯得實際得多。我們使用無母數迴歸來估計測量誤差的變異數,並在小測量誤差的假設下,以泰勒展開式近似原始的分數函數,以及母體總數的估計量,除此之外不需其他太多假設。當測量誤差的變異數趨近於0時,我們的估計方法會趨近於使用原始條件概似函數的估計方法,由於我們的修正方法相當有彈性,可以很容易地修改並應用於其他的重複捕取模型。最後,我們利用電腦模擬評估我們所提議的估計方法。

關鍵字

異質性 ； 測量誤差 ； 無母數迴歸

並列摘要

In this paper, we consider the estimation of discrete time capture-recapture model when covariate is subject to heterogeneous measurement error. There are two reasons for considering heterogeneous error in the capture-recapture experiments. One reason is for the possibility that the magnitude of the measurement error may depend on the true covariate, and the other reason is for the numbers of replicate measurements in each individual can be very different. Thus, a heterogeneous error assumption is more practical than the homogeneous error assumption which was adopted by most literatures. We used a nonparametric regression to estimate the variance of measurement error,
and used Taylor polynomial to estimate the original score function and population size estimator under small measurement error assumption. There are not much assumptions required to implement the proposed method.
Our estimation will reduce to the conditional likelihood approaches when the error's variance approaches 0, and is easy to modify at least in theory to accommodate many kinds of heterogeneous error or capture-recapture models.Some simulation studies were conducted to assess the performances of the proposed estimation.

並列關鍵字

heterogeneous ； measurement error ； nonparametric regression

參考文獻

陳飛穎 (2005) 重複捕取實驗中自變數有測量誤差時的近似估計方法,中華民國碩士論文。

Huggins, R. M. (1989). On the statistical analysis of capture experiments. Biometrika 76, 133-140.

Hwang, W. H. and Huang, S. Y. H. (2003). Estimation in capture-recapture models when covariates are subject to

measurement errors. Biometrics 59, 1115-1124.

Hwang, W. H., Huang, S. Y. H., and Wang C. Y. (2005). Effects of measurement error and conditional score estimation