在測量誤差模式中,當解釋變數與測量誤差皆為常態分配時,線性與 probit 模式皆是不可辨認的,因此過去文獻所提出的分析方法幾乎都要求有額外的訊息或假設,以避免模式的不可辨認性方能進行分析。但我們認為模式的不可辨認性應屬少數的特例,在大多數的情形即使沒有額外訊息還是可以發展具有一致性的分析方法。在無額外的訊息之下, 本文提出使用過量參數的估計方法,並從理論上驗證參數何時會具有一致性的估計量。另外電腦的模擬結果也與理論上的期望相吻合。

When measurement errors are present, the linear model and probit model are unidentifiable if the covariate is normally distributed. Thus, one usually requires extra information or assumptions to proceed the analysis. However, we think that the unidentifiability are special cases and will not happen for other distributions of the covariate. When there is no extra information, we propose an overparameterization method to estimate the regression parameters and the variance of the measurement error. We provide a theoretical verification and a conjecture for when the model can be analyzed consistently by the proposed method. A simulation study was conducted and seems to be coincided with the theoretical results.

1.緒論                                                   1

2.文獻回顧(傳統上有測量誤差的處理方法)                   3
  2.1 不可辨認性(unidentifiability)......................3 
  2.2 傳統上線性模式有測量誤差時的處理方法...............5
  2.3 傳統上probit模式有測量誤差時的處理方法.............7

3.無額外訊息下的估計方法                                 9
  3.1 過量參數法概念.....................................9
  3.2 當測量誤差變異數未知時,線性模式無額外訊息的估計方法
      ...................................................10
  3.3 當測量誤差變異數未知時,probit模式無額外訊息的估計方法
      ...................................................13

4.模擬的過程與結果                                       15
  4.1 線性模式的模擬結果.................................15
  4.2 probit 模式的模擬結果..............................16
5.結論                                                   18
參考文獻                                                 20
附錄                                                     22

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