臺灣博碩士論文加值系統

　平均值函數（mean functions）在多維分析上的檢定是很重要的一部份，以變異數分析．共變異數分析和迴歸分析作為應用的基礎,有關這個問題的檢定在隨機過程的資料中是比較少被研究．
　在這篇論文中，我們將討論布朗運動之線性和二次動向函數的同值檢定．

　Testing equality of mean functions is important in multivariate analysis.The application can be found in analysis of variance,analysis of covariance and regression.However,this testing problem is relatively less explored for stochastic processes datum.In this paper,we present homogeneous tests for linear quadratic drift functions of Brownian motions.

Contents
1.Introduction.....................................................1
2.Homogeneous Tests for Linear Mean functions......................3
2.1 Homogeneous Tests for Two Parameters........................6
2.2 Homogeneous Tests for Intercepts...........................22
2.3 Homogeneous Tests for Slopes...............................31
3.Homogeneous Tests for Quadratic Mean functions..................40
3.1 Homogeneous Tests for Three Parameters.....................44
3.2 Homogeneous Tests for a and b..............................64
3.3 Homogeneous Tests for b and r..............................77
3.4 Homogeneous Tests for a and r..............................90
3.5 Homogeneous Tests for a...................................103
3.6 Homogeneous Tests for b...................................116
3.7 Homogeneous Tests for r...................................129
4.Conclusion.....................................................142
.Reference.......................................................147

[1] Andersen, P. K. Borgan, O. Gill, R.D. and Keiding, N.(1993). Statistical Methods
on Counting Processes. Springer-Velag.
[2] Anderson, T.W. (1984). An Introduction to Multivariate Statistical Analysis. 2nd
ed. Wiley.
[3] Bosq, D.(1998). Nonparametric Statistic Stochastic Process. 2nd. ed., Lecture
Notes in Statistics 110. Springer.
[4] Basawa, I.V. and Prabhu, N.U. (1994). Statistical Inference in Stochastic Pro-
cesses. Special issue of Journal of Statistical Planning and Inference, 39.
[5] Breslow, N. E. (1970). A Generalized Kruskal-Wallis Test for Comparing K Sam-
ples Subject to Unequal Patterns of Censorship. Biometrika 57 ,579-594.
[6] Basawa, I.V. and Prakasa Rao, B.L.S. (1980). Statistical Inference for Stochastic
Processes, Academic Press, London.
[7] Billingsley, P. (1961). Statistical Inference for Markov Processes. University of
Chicago Press, Chicago.
[8] Beran, J. (1994). Statistical Methods for Long Memory Processes. Chapman and
Hall, London .
[9] Cox, D. R. and Lewis, P. A. W. (1978). The Statistical Analysis of Series of
Events. Chapman and Hall.
[10] Delgado, M.A. (1993). Testing the Equality of Nonparametric Regression Curves.
Statist. Probab. Lett.,17, 199-204.
[11] Dette, H. and Munk, A. (1998). Nonparametric Comparison of Several Regression
Functions: Exact and Asymptotic Theory. Ann. Statist.,26, 2339-2368.
[12] Dette H. and Neumeyer N. (2001). Nonparametric Analysis of Covariance. Ruhr-
UniversitÄat Bochum. Ann. Statist. Vol. 29, No. 5, 1361-1400.
[13] Fleming, T. R. and Harrington, D. P.(1991). Counting Processes and Survival
Analysis. Wiley.
[14] Guttorp, P.(1991). Statistical Inference for Branching Processes. Wiley.
[15] Gehan, E. A. (1965). A Generalized Wilcoxon Test for Comparing Arbitrarily
Singly Censored Samples. Biometrika 52 ,203-223.
[16] Grenander, U. (1981). Abstract Inference. Wiley.
[17] HÄardle, W. and Marron, J.S. (1990). Semiparametric Comparison of Regression
Curves. Ann. Statist.,18, 63-89.
[18] Hogg, R. V. and Craig, A. T. (1995). Introduction to Mathematical Statistics.
5nd ed., Prentice Hall.
[19] Klein J. P. and Moeschberger M. L. (1997). Survival Analysis. Medical College
of Wisconsin and The Ohio State University Medical Center.
[20] Kutoyants, Yu.A. (1984). Parameter Estimation for Stochastic Processes (trans.
and ed. B.L.S. Prakasa Rao), Heldermann, Berlin.
[21] Kutoyant, Y.A. (2004). Statistical Inference for Ergodic Di®usion Processes.
Spriner.
[22] King, E.C., Hart, J.D. and Wehrly, T.E. (1991). Testing the Equality of Regres-
sion Curves Using Liner Smoothers. Statist. Probab. Lett.,12, 239-247.
[23] Karr, A. F. (1991). Point Processes and their Statistical Inference. Marcel
Dekker, New York.
[24] Prakasa Rao, B.L.S. (1999a). Statistical Inference for Di®usion Type Process.
Arnold.
[25] Prakasa Rao, B.L.S. (1999b). Semimartingales and their Statistical Inference.
Chapman and Hall.
[26] Prakasa Rao, B.L.S. and Bhat, B.R. (1996). Stochastic Processes and Statistical
Inference. New Age International, New Delhi.
[27] Prabhu, N. U., ed. (1988). Statistical Inference from Stochastic Processes. (Con-
temporary Mathematics, Vol. 80 ). American Mathematical Society, Providence,
RI.
[28] Prabhu, N. U. and Basawa, I. V. (1991). Statistic Inference in Stochastic Pro-
cesses. Marcel Dekker, New York.
[29] Su, S.T. (2004). ANOVA for Constant Means of Brownian motions and Poisson
Processes. Master Thesis, National Central University.
[30] Shorack, G. and Wellner, J. A. (1986). Empirical Processes with Applications to
Statistics. Wiley.
[31] Taniguchi, M. and Kakizawa, Y. (2000). Asymptotic Theory of Statistical Infer-
ence for Time Series. Springer.
[32] Tarone, R. E. and Ware, J. H. (1977). On Distribution-Free Tests for Equality
for Survival Distributions. Biometrika ,64,156-160.