二項式分配線性組合之預測區間

在預測未來觀測值的研究方法裡，預測區間是一個非常實用的方法。不論是在工業上的應用或是醫學領域上的應用，預測區間都能夠實際的應用在這些領域中。由於現有的文獻研究著重於連續型的預測區間以及單一離散型變量的預測區間之應用，這些現有的方法，可能無法直接應用到多變量的狀況。因此，在這篇論文裡，我們所探討的預測區間是在多變量的伯努力分配變數之線性組合的應用。我們主要考量兩大方向：(1)在不同變數下，參數間具有某一相關，(2)在不同變數下，參數之間無特定相關。這個研究方法主要是延伸Wang(2010)所提出的預測區間的方法。我們並以模擬結果來檢驗所提出的預測區間之優劣。

關鍵字

覆蓋率；二項式分配；預測區間

並列摘要

The prediction interval is a useful tool to predict the future observations. It can be widely used in industrial and medical applications. Although there are some previous studies focusing on the construction of prediction intervals for continuous distribution or some previous studies focusing on the construction of prediction intervals for discrete distribution of single variable, these meth- ods cannot be directly applied to construct prediction interval for functions of multiple variables. In this thesis, we investigate prediction intervals for a linear function of binomial random variables. We consider two cases: (1) there is a relationship of parameters for dierent variables, and (2) there is no any relationship of parameters for dierent variables. The proposed method is an extension of Wang (2010). A simulation result shows the performance of the proposed method.

並列關鍵字

Coverage probability ； Binominal distribution ； Prediction interval

參考文獻

[1] Bain, L. J., and Patel, J. K. (1993). Prediction Intervals Based on Partial Observations for Some Discrete Distributions, IEEE ransactions on Reliability, 42,459-463.

[2] Basu, R., Ghosh, J.K., Mukerjee, R. (2003). Empirical Bayes Prediction Intervals in Normal Regression Model: Higher Order Asymptotics, Statistics and Probability Letters, 63, 197-203.

[3] Hall, P., and Rieck, A. (2001), Improving Coverage Accuracy of Nonparametric Prediction Intervals. Journal of the Royal Statistical Society, Ser. B, 63, 717-725.

[4] Hamada, M., Johnson, V., Moore, L. M., and Wendelberger, J. (2004). Bayesian Prediction Intervals and Their Relationship to Tolerance Intervals, Technometrics, 46, 452-459.

[5] Lawless, J. F., and Fredette, M. (2005). Frequentist Prediction Intervals and Predictive Distributions, Biometrika, 92, 529-542.

國際替代計量

二項式分配線性組合之預測區間

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