臺灣博碩士論文加值系統

在本文中，我們討論當採用集合排序樣本，關於常態平均值的檢定問題。透過模擬的結果發現，本文所提的採集合排序樣本檢定，會優於傳統所用的 Z 或 t 檢定。另外我們也提供使用採集合排序樣本檢定時所需的臨界值表格。

In this thesis, we address the problems of testing the normal mean with ranked-set samples.
We find the RSS-based tests outperform substantially usual Z- or t-tests through simulations. Tables of the cutoff points for using the RSS-based tests are also provided.

Content

1 Introduction
2 Main Results
2.1 One-sided Problem
2.1.1 Known Variance Case
2.1.2 Unknown Variance Case
2.2 Two-sided Problem
2.2.1 Known Variance Case
2.2.2 Unknown Variance Case
2.3 Discussion
3 Conclusion

Bickel, P.J. (1967)
Some contributions to the theory of order statistics.
Proc. 5th Berkeley Symp., 1, 575-591.

Bose, R.C. and Gupta, S.S. (1959)
Moments of order statistics from a normal population.
Biometrika, 46, 433-440.

David, H.T. (1963)
The sample mean among the extreme normal order statistics.
Ann. Math. Statist., 34, 33-35.

David, H.A. and Levine, D.N. (1972)
Ranked set sampling in the presence of judgement error.
Biometrics, 28, 553-555.

Dell, T.R. (1969)
The theory of some applications of ranked set sampling.
Ph.D. thesis, University of Georgia, Athens, GA.

Dell, T.R. and Clutter, J.L. (1972)
Ranked set sampling theory with order statistics background.
Biometrics, 28, 545-555.

Koti, K.M. and Babu, G.J. (1996).
Sign test for ranked-set sampling.
Communication in Statistics-Theory and Methods, 25, 1617-1630.

McIntyre, G.A. (1952).
A method for unbiased selective sampling, using ranked sets.
Australian J. Agricultural Research, 3, 385-390.

Patil, G.P., Sinha, A.K. and Taillie, C. (1994)
Ranked set sampling.
In The Handbook of Environmental Statistics, Volume 12.
North Holland: Elsevier Science Publishers.

Ridout, M.S. and Cobby, J.M. (1987)
Ranked set sampling with non-random selection of sets and errors in ranking.
Appl. Statist., 36, No.2, 145-152.

Roussas, G. (1997)
A course in mathematical statistics, 2nd ed.
Academic Press.

Sinha, B.K., Sinha, B.K. and Purkayastha, S. (1996).
On some aspects of ranked set sampling for estimation of normal and exponential parameters.
Statistics and Decision, 14, 223-240.

Tukey, J.W. (1958)
A problem of Berkson, and minimum variance orderly estimators.
Ann. Math. Statist., 29, 588-592.

Yu, P.L.H. and Lam, K. (1997)
Regression Estimator in ranked set sampling.
Biometrics, 53, 1070-1080.