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研究生:蘇煒盛
研究生(外文):Wei-Sheng Su
論文名稱:區間假設最大概似比檢定與學生化全距檢定的比較
論文名稱(外文):A Comparison of Maximum Likelihood Ratio Test and Studentized Range Test for Interval Hypotheses
指導教授:陳順益陳順益引用關係
學位類別:碩士
校院名稱:淡江大學
系所名稱:數學學系碩士班
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:65
中文關鍵詞:點假設檢定學生化全距檢定最保守均數結構最大概似比檢定
外文關鍵詞:Point HypothesisStudentized Range TestLeast Favorable ConfigurationMaximum Likelihood Ratio Test
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變異數已知或未知情況下,探討兩組或多組母體平均數是否具有差異性,傳統方法是用點假設檢定。然而在點假設檢定中,只要樣本數夠大,就會拒絕虛無假設。因為點假設檢定這個缺點,許多研究都利用區間假設檢定來取代。其中,Bau, Chen 和 Xiong(1993)的學生化全距檢定只適用最保守均數結構,可是實際統計資料並不太可能符合此結構。本文根據Chen 和 Hsu(2005) 所導出的最大概似比檢定法來改進此缺點。本文並以蒙地卡羅模擬方法來比較最大概似比檢定法和Bau, Chen 和 Xiong(1993) 學生化全距檢定法及Casella和Berger(1990) 交聯集檢定法的顯著水準和檢定力。就兩組母體(K=2)而言,最大概似比檢定法和學生化全距檢定法及交聯集檢定法的名目 水準均發生在邊界上,而檢定力的表現是差不多的。就三組母體(K=3)而言,全距檢定法只有在LFC結構下,才有名目 水準;而最大概似比檢定法在任何資料結構下均有名目 水準,較合乎實際情況。就檢定力來說,最大概似比檢定法的檢定力均比全距檢定法大。
In the classical hypothesis testing concerning several normal means the interest is to test the null hypothesis that the population means are equal. However, it is well known that the null hypothesis will always be rejected for a large enough sample size (See Berger (1985)). Recently, the problem of testing the hypothesis of equivalence of normal means (or the interval hypothesis) has been investigated by several authors. In this paper, an extensive simulation study was carried out to compare the performance of the likelihood ratio test of Chen and Hsu (2005), the studentized range test of Bau, Chen and Xiong (1993), and the intersection-union test of Casella and Berger (1990). The simulation results indicate that, for two populations (K=2), the nominal significance levels of all three tests occur at the boundary, and the performance of powers are similar. For the case of three populations (K=3), the nominal level of the studentized range test occurs only under the least favorable configuration of means. The likelihood ratio test can achieve the nominal level for any configuration of means and its power is larger than that of the studentized range test.
1 前言1
2 文獻回顧3
2.1 學生化全距檢定(studentized range test) 程序. . . 3
2.2 交聯集檢定(intersection-union test) 程序. . . . . 6
3 最大概似比檢定法9
3.1 二個母體(k=2) . . . . . . . . . . . . . . . . . . . 9
3.1.1 變異數已知 . . . . . . . . . . . . 9
3.1.2 變異數未知. . . . . . . . . . . . . 10
3.2 三個母體(k=3) . . . . . . . . . . . . . . . . . . . 11
3.2.1 變異數已知, r2 已知. . . . . . . 11
3.2.2 變異數已知, r2 未知. . . . . . . 12
3.2.3 變異數未知, r2 已知. . . . . . . . . . . . . 13
3.2.4 變異數未知, r2 未知. . . . . . . . . . . . . 13
4 模擬研究15
5 結論54
1. Bau, J.J., Chen, H.J., and Xiong, M., (1993). ”Percentage
Points of the Studentized Range Test for Dispersion of
Normal Means”. J. Statist. Comput. Simul., Vol. 44. pp.
149-163
2. Berger, J.,(1985). ”Statistical Decision Theory and Bayes
ian Analysis”. New York :Springer-Verlag
3. Berger, R.L., (1982). ”Multiparameter Hypoththesis Testing
and Acceptance Sampling”. Technometrics., Vol. 24.
pp. 295-300
4. Berger, R.L., and Hsu, J.C., (1996). ”Bioequivalence Trials,
Intersection-Union Tests and Equivalence Confidence
Sets”. Statistical Science, Vol.11, pp. 283-319
5. Bofinger, E., Hayter, A.J., and Liu, W., (1993). ”The
Construction of Upper Confidence Bounds on the Range
of Several Location Parameters”. Journal of the American
Statistical Association, Vol. 88, pp. 906-911
6. Casella, G., and Berger, R.L., (1990). ”Statistical Inference”.
Wadsworth and Brooks/Cole, Pacific Grove, CA.
7. Chen, H.J., Lam, K. and Xiong, M., (1990). ”Infernece
on the dispersion of several location parameters.” Technical
Report 157, Department of Statistics, University of
Georgia, Athens, Georgia. (Submitted to the Journal of
the Statistical Planning and Influence).
8. Chen, S.Y., and Hsu, C.F., (2005). ”The Maximum Likelihood
Ratio Tests for Equivalence Test”. unpublished manuscript.
9. Chow, S.C., and Liu, J.P., (1992). ”Design and Analysis
of Bioavailiability and Bioequivalence Studies”. New York
:Marcel Dekker.Inc
10. David, H.A., Lachenbruch, P.A., and Brandis, H.P. (1972).
”The Power Function of Range and Studentized Range
Tests in Normal Samples”. Biometrika 59, 161-168.
11. Hayter, A.J., and Liu, W., (1990). ”The Poewr Function
of the Studentised Range Test”. The Annals of Statistics,
Vol. 18, pp. 465-468
12. Kastenbaum, M.A., Hole, D.G., and Bowman, K.O. (1970).
”Sample Size Requirements: One-Way Analysis of Variance.”
Biometrika 57, 421-430.
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