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研究生:李根良
研究生(外文):Gen-liang Li
論文名稱:四捨五入型資料參數估計之研究
論文名稱(外文):A study on the parameter estimation based on rounded data
指導教授:郭美惠郭美惠引用關係
指導教授(外文):Mei-Hui Guo
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:61
中文關鍵詞:捨入型資料A-K 調整估計值近似最大概似估計值SOS 估計值ARMA 模型變異數降低法
外文關鍵詞:A-K corrected estimatorApproximate MLEARMA(p,q) modelRounded dataSOS estimatorVariance reduction
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在日常生活中,許多連續型資料由於記錄機制的精確性,記錄值常被捨入到小數位。而這些捨入誤差將影響測量和估計的準確性。本研究介紹三種對於捨入型資料參數估計的方法,分別是 A-K 調整估計法、近似最大概似估計值 和 SOS 估計法,並且比較三種方法估計值的表現。為了進行比較,我們先推導在 MA(1) 模型的 A-K 調整估計值。另一方面,為了提高估計上的效率,利用上述三種估計值作線性組合,提出了兩種變異數降低法,得到一個新的不偏估計值。模擬結果顯示,新提出的降低變異數的估計值顯著提升估計的效率性。
Most recorded data are rounded to the nearest decimal place due to the precision of the recording mechanism. This rounding entails errors in estimation and measurement. In this paper, we compare the performances of three types of estimators based on rounded data from time series models, namely A-K corrected estimator, approximate MLE and the SOS estimator. In order to perform the comparison, the A-K corrected estimators for the MA(1) model are derived theoretically. To improve the efficiency of the estimation, two types of variance-reduction estimators are further proposed, which are based on linear combinations of aforementioned three estimators. Simulation results show the proposed variance reduction estimators significantly improve the estimation efficiency.
論文審定書 i
謝誌 ii
摘要 iii
Abstract iv
1 Introduction 1
2 Literature Review 3
2.1 A-K correction method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Approximate MLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 AMLE: AR(1) model . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 AMLE: MA(p) model . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 SOS method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Modified SOS method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Newly proposed estimators 13
3.1 A-K correction of MA(1) model . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Variance reduction techniques . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 Simulation study 17
4.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 AR(1) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 MA(1) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4 AR(2) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5 ARMA(1,1) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 Conclusion 23
A Appendix 24
A.1 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
A.1.1 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
A.1.2 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
A.1.3 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.1.4 Proof of Lemma 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
A.1.5 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
A.2 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
A.3 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
References 50
1. Bai, Z. D., Zheng, S. R., Zhang, B. X., Hu, G. R., (2009). Statistical analysis for rounded data. Journal of Statistical Planning and Inference, 139, 2526-2542.
2. Box, G. E. P., Jenkins, G. M., (1976). Time Series Analysis: Forecasting and Control, Revised Edition. Holden-Day, CA.
3. Dempster, A. P., Rubin, D. B., (1983). Rounding error in regression: The appropriateness of sheppard''s corrections. Journal of the Royal Statistical Society, Series B, 45, 51-59.
4. Durrans, S. R., Pitt, R., (2004). Maximum likelihood estimators for coarsely resolved precipitation data. Journal of Hydrologic Engineering, 9, 13-27.
5. Grimshaw, S. D., McDonald, J., McQueen, G. R., Thorley, S., (2005). Estimating hazard functions for discrete lifetimes. Communications in Statistics, Part B-Simulation and Computation, 34, 451-463.
6. Hall, P., (1982). The influence of rounding errors on some nonparametric estimators of a density and its derivatives. SIAM Journal on Applied Mathematics, 42, 390-399.
7. Heitjan, D. F., Rubin, D. B., (1991). Ignorability and coarse data. The Annals of Statistics, 19, 2244-2253.
8. Jones, R. H., (1980). Maximum likelihood fitting of ARMA models to time series with missing bservations. Technometrics, 22, 389-395.
9. Kozicki, S., Hoffman, B., (2004). Rounding error: a distorting influence on index data. Journal of Money, Credit, and Banking, 36, 319-338.
10. Lee, C. S., Vardeman, S. B., (2001). Interval estimation of a normal process mean from rounded data. Journal of Quality Technology, 33, 335-348.
11. Lee, C. S.,Vardeman, S. B., (2002). Interval estimation of a normal process standard deviation from rounded data. Communications in Statistics, Part B-Simulation and Computation, 31, 13-34.
12. Lee, C. S., Vardeman, S. B., (2003). Confidence interval based on rounded data from the balanced one-way normal random effects model. Communications in Statistics, Part B-Simulation and Computation, 32, 835-856.
13. Lindley, D. V., (1950). Grouping corrections and maximum likelihood equations. Proceedings of the Cambridge Philosophical Society, 46, 106-110.
14. McCullough B. D., Vinod H. D., (1999). The Numerical Reliability of Econometric Software, Journal of Economic Literature, 37, 633-665.
15. Rose, E. L., (1993). Some effects of rounding errors on ARMA (1,1) models. Communications in Statistics, Part B-Simulation and Computation, 22, 155-174.
16. Ross S. M., (2006). Simulation, 4th Edition. Elsevier, Acad. Press.
17. Sheppard W. F., (1898). On the calculation of the most probable values of frequency constants for data arranged according to equidistant divisions of a scale. Proceedings of the London Mathematical Society, 29, 353-380.
18. Skeel, R., (1992). Roundoff Error and the Patriot Missile. SIAM News 25, 11.
19. Stam, A., Cogger, K. O., (1993). Rounding errors in autoregressive processes. Internatonal Journal of Forecasting, 9, 487-508.
20. Tallis, G. M., (1967). Approximate maximum likelihood estimates from grouped data. Technometrics, 9, 599-606.
21. Tricker T., (1984). Effects of rounding data sampled from the exponential distribution. Journal of Applied Statistics, 11, 54-87.
22. Tricker, A. R., (1990a). The effect of rounding on the power level of certain normal test statistics. Journal of Applied Statistics, 17, 219-228.
23. Tricker, A. R., (1990b). The effect of rounding on the significance level of certain normal test statistics. Journal of Applied Statistics, 17, 31-38.
24. Tricker, A. R., (1992). Estimation of parameters for rounded data from non-normal distributions. Journal of Applied Statistics, 19, 465-471.
25. Tsay, R. S., (2005). Analysis of financial time series, 2nd Edition. Wiley, Hoboken, New Jersey.
26. United Stated General Accounting Office, (1992). GAO/IMTEC-92-26 Patriot Missile Software Problem. URL http://www.fas.org/spp/starwars/gao/im92026.htm.
27. Vardeman, S. B., Lee, C. S., (2005). Likelihood-based statistical estimation from quantization data. IEEE Transactions on Instrumentation and Measurement, 54, 409-414.
28. Wei, W.S., (2006). Time series analysis : univariate and multivariate methods, 2nd Esition. Pearson Addison Wesley, Boston.
29. Zhang, B. X., Liu, T. Q., Bai, Z. D., (2010). Analysis of rounded data from dependent sequences. Ann. I. Statist. Math., 62, 1143-1173.
30. 黃文璋,(2003)。``機率論'',華泰書局。
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