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題名 Simultaneous Confidence Intervals and Multiple Tests for Multinomial Proportions
作者 侯家鼎
Hou, Chia-Ding
貢獻者 戴政<br>江振東
Tai, John Jen<br>Chiang, Jeng-Tung
侯家鼎
Hou, Chia-Ding
日期 1997
上傳時間 14-四月-2016 13:57:19 (UTC+8)
摘要 Let us outline the contents of the chapters to follows.
參考文獻 REFERENCES
     Agresti, A. (1984). Analysis of Ordinal Categorical Data. New York: John Wiley.
     Agresti, A. (1990). Categorical Data Analysis. New York: John Wiley and Sons.
     Angers, C. (1984). Large sample sizes for the estimation of multinomial frequencies
     from simulation studies. Simulation, 10, 175-178.
     Ardisia, c., Venti, G., Colozza, M.A., Breschi, c., Porfirio, B. , Davis, S., Tonato, M.,
     Donti, E. (1993). Expression of aphidicolin-induced fragile sites in lymphocytes of
     patients with breast cancer. Cancer Genet Cytogenet, 67, 113-116.
     Bakir, M. A., Byrne, M. D. (1994). An application of the multi-stage Monte Carlo
     optimization algorithm to aggregate production planning. International Journal of
     Production Economics, 35, 207-213 .
     Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975). Discrete Multivariate
     Analysis: Theory and Practice. Cambridge, MA, The MIT Press.
     Bohn, U., Dahm, P. F., McAllister, B. F., Greenbaum, I. F. (1995). Identifying
     chromosomal fragile sites from individuals: a multinomial statistical model. Hum
     Genet, 95, 249-256.
     Cochran, W. G. (1963). Sampling Techniques (2nd ed.), New York: 10lm Wiley.
     Cressie, N., Read, T. R. C. (1984). Multinomial goodness-of-fit tests. Journal of the
     Royal Statistical Society Series B 46,440-464.
     Cressie, N., Read, T. R. C. (1988) . Goodness-of-Fit Statistics for Discrete
     Multivariate Data, New York: Springer-Verlag.
     De Braekeleer, M. (1987). Fragile sites and chromosomal structure rearrangements in
     human leukemia and cancer. Anticancer Res., 7,417-422.
     De Braekeleer, M. (1989). Fragile sites and statistics. Hum Genet, 84, 103.
     De Braekeleer, M., Smith, B. (1988). Two methods for measuring the nonrandomness
     of chromosome abnormalities. Ann hum Genet 52 , 63-67.
     Ethier, S. N. (1982 ). Testing for favorable numbers on a roulette wheel. Journal of the American Statistical Association, 77, 660-665.
     Fienberg, S. E. (1980). The Analysis of Cross-Classified Categorical Data (2nd ed.).
     Cambridge, MA, the MIT Press.
     Fitzpatrick, S., Scott, A. (1987). Quick simultaneous confidence intervals for
     multinomial proportions. Journal of the American Statistical Association ., 82, 875-
     878.
     Freeman, D. H. (1987). Applied Categorical Data Analysis. New York, Marcel
     Dekker.
     Fuchs, c., Kenett, R. (1980). A test for detecting outlying cells in the multinomial
     distribution and two-way contingency tables. Journal of the American Statistical
     Association, 75, 395-398.
     Glaz, J., Johnson, B. (1984). Probability for multivariate distributions with
     dependence structures. Journal of the American Statistical Association, 79, 436-441.
     Gold, R. Z. (1963). Tests auxiliary to %2 tests in a Markov chain. Ann. Math. Statist.,
     34, 56-74.
     Goodman, L. A. (1965). On simultaneous confidence intervals for multinomial
     proportions. Technometrics, 7,247-254.
     Haberman, S. J. (1974) . The Analysis of Frequency Data. Chicago, University of
     Chicago Press.
     Hecht, F., Glover, T. W. (1984). Cancer chromosome breakpoints and common fragile sites induced by aphidicolin. Cancer Genet Cytogenet., 13, 185-188.
     Hecht, F., Sutherland, G. R. (1984). Fragile sites and cancer breakpoints. Cancer
     Genet Cytogenet, 12,179-181.
     Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of
     significance. Biometrika, 75,800-802.
     Holm, S. (1979). A simple sequentially rejective multiple test procedure.
     Scandinavian Journal of Statistics, 6, 65-70.
     Hurtubise, R. (1969). Sample sizes and confidence intervals associated with a Monte
     Carlo simulation model possessing a multinomial output. Simulation, 12, 71-77.
     ISCN. (1981). An international system for human cytogenetic nomenclature?high
     resolution banding. Cytogenet Cell Genet, 31, 1-23.
     JOMson, N. L., Kotz, S. (1970).Continuous Univariate Distributions-2. Houghton
     Mifflin, Boston.
     Jordan, D. K. , Bums, T. W., Divelbiss, J. E., Woolson, R. F., Patil, S. R. (1990) .
     Variability in expression of COnU1lOJ1 fragile sites: in search of a new criterion. Hum Genet, 85,462-466.
     Jowett, G. H. (1963). The relationship between the binomial and F distribution.
     Statistician, 13,55-57.
     Koehler, K., Larntz, K. (1980). An empirical investigation of goodness-of-fit statistics
     for sparse multinomials. Journal of the American Statistical Association, 75,336-344.
     Le Beau, M. M. (1986). Chromosomal fragile sites and cancer-specific· .
     rearrangements. Blood, 67, 849-858.
     Le Beau, M. M., Rowley, J. D. (1984). Heritable fragile sites and cancer. Nature, 308,
     607-608.
     Levin, B. (1981). A representation for multinomial cumulative distribution functions.
     The Annals of Statistics, 9,1123-1126.
     Mariani, T. (1989a). Fragile sites and statistics. Hum Genet, 81, 319-322.
     Mariani, T. (1989b). Reply to letter by M. De Braekeleer. Hum Genet, 84, 104.
     Mehta, C. R., Patel, N. R. , Senchaudhuri, P. (1988). Importance sampling for
     estimating exact probabilities in permutational inference. Journal of the American
     Statistical Association, 83,999-1005.
     Miller, R. G., Jr. (1977). Developments in mUltiple comparisons 1966-l976 . .Tournai
     of the American Statistical Association, 72, 779-788.
     Miller, R. G., Jr. (1981). Simultaneous Statistical Inference (2nd ed.). New York:
     Springer-Verlag.
     Nelson, L. S. (1995). The usefulness of Monte Carlo tests. Journal of Quality
     Technology, 27, 387-389.
     Quesenberry, C. P., Hurst D. C. (1964). Simultaneous confidence intervals for
     multinomial proportions. Technometrics, 6, 191-195.
     Roy, S. N. (1953). On a heuristic method of test construction and its use in
     multivariate analysis. Ann. Math. Stat., 24, 220-238.
     Seber, G. A. (1977). Linear regression analysis. Wiley, New York.
     Sison, C. P., Glaz, 1. (1995). Simultaneous confidence intervals and sample size
     determination for multinomial proportions. Journal of the American Statistical
     Association, 90, 366-369.
     Smith, CAB. (1986). Chi:`squared tests with small numbers. Ann hum Genet, 50, 163-
     167.
     Sobol, J. M. (1974). The Monte Carlo Method. The University of Chicago Press.
     Sutherland, G. R., Ledbetter, D. H. (1989). Report of the committee on cytogenetic
     markers. Tenth International Workshop on Human Gene Mapping. Cytogenet Cell
     Genet, 51, 452-458.
     Tai,J. J., Hou, C-D., Wang-Wuu, S., Wang, C-H., Leu, S-Y., Wuu, K-D. (1993). A
     method for testing the nonrandonmess of chromosomal breakpoints. Cytogenet Cell
     Genet, 63,147-150.
     Tarone, R. E. (1989). Testing for nonrandol111less of events in sparse data situations.
     Ann hum Genet, 53,381-387.
     Thompson, E. A. (1994). Monte Carlo likelihood in genetic mapping. Statistical
     Science, 9, 355-366.
     Thompson, S. K. (1987). Sample size for estimating multinomial proportions. The
     American Statistician, 41 , 42-46.
     Tortora, R. D. (1978) . A note on sample size estimation for multinomial populations.
     The American Statistician, 32, 100-102.
     Troendle, J. F. (1995). A stepwise resampling method of multiple hypothesis testing.
     Journal of the American Statistical Association, 90, 370-378.
     Vasarhelyi, K., Friedman, J. M. (1989). Analyzing rearrangement between breakpoint
     distributions by means of binomial confidence intervals. Ann hum Genet, 3,375-380.
     Wang, C-H. , Leu, S- Y., Tai, J. J., Wuu, K-D., Wang-Wuu, S. (1992). Chromosomal
     fragile sites expression in lymphocytes of patients ,,with colorectal carcinoma and of
     healthy controls. Ms. Submitted for publication.
     Zar, J. H. (1984). Biostatistical Analysis. Prentice-Hall, Englewood Cliffs.
描述 博士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002000636
資料類型 thesis
dc.contributor.advisor 戴政<br>江振東zh_TW
dc.contributor.advisor Tai, John Jen<br>Chiang, Jeng-Tungen_US
dc.contributor.author (作者) 侯家鼎zh_TW
dc.contributor.author (作者) Hou, Chia-Dingen_US
dc.creator (作者) 侯家鼎zh_TW
dc.creator (作者) Hou, Chia-Dingen_US
dc.date (日期) 1997en_US
dc.date.accessioned 14-四月-2016 13:57:19 (UTC+8)-
dc.date.available 14-四月-2016 13:57:19 (UTC+8)-
dc.date.issued (上傳時間) 14-四月-2016 13:57:19 (UTC+8)-
dc.identifier (其他 識別碼) A2002000636en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/84404-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) Let us outline the contents of the chapters to follows.en_US
dc.description.tableofcontents TABLE OF CONTENTS
     CHAPTER
     Ⅰ．INTRODUCTION..........1
     Ⅱ．SIMULTANEOUS CONFIDENCE INTERVALS FOR MULTINOMIAL PROPORTIONS..........3
     2.1 Introduction..........3
     2.2 Review of the Published Procedures..........5
     2.3 The First Alternative Method for Constructing Simultaneous Confidence Intervals for Multinomial Proportions..........8
     2.4 The Second Alternative Method for Constructing Simultaneous Confidence Intervals for Multinomial Proportions..........11
     2.4.1 The Derivation of the Method..........11
     2.4.2 The Best Power-Divergence Simultaneous Confidence Intervals..........20
     2.5 Simulation Study..........22
     2.5.1 Numerical Comparisons of Coverage Probabilities and Volumes among Different Methods..........24
     2.5.2 Numerical Comparisons in Sparse Data Situations..........28
     2.6 A Brief Discussion for the Possible Improvement on the Best Power-Divergence Simultaneous Confidence Intervals..........34
     2.7 Concluding Remarks..........37
     Ⅲ．MULTIPLE TESTS AND ITS APPLICATION TO IDENTIFICATION OF CHROMOSOMAL FRAGILE SITES..........38
     3.1 Introduction..........38
     3.2 Review of the Published Procedures..........39
     3.3 Testing the Nonrandomness Chromosomal Breakpoints Using Largest Order Statistics..........46
     3.3.1 Under the Proportional Probability Model..........46
     3.3.2 Under the Equiprobability Model..........50
     3.4 Numerical Study..........51
     3.5 Identifying Chromosomal Fragile Sites from a Hierarchical Clustering Point of View..........64
     3.5.1 Perliminaries..........64
     3.5.1.1 Union-Intersection Principle..........64
     3.5.1.2 Hochberg’s Step-Up Multiple Hypothesis Testing Algorithm..........65
     3.5.2 Main Results..........66
     3.6 Numerical Study..........69
     Ⅳ．SUMMARY AND DIRECTION FOR FURTHER RESEARCH..........77
     REFERENCES..........80		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002000636en_US
dc.title (題名) Simultaneous Confidence Intervals and Multiple Tests for Multinomial Proportionsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) REFERENCES
     Agresti, A. (1984). Analysis of Ordinal Categorical Data. New York: John Wiley.
     Agresti, A. (1990). Categorical Data Analysis. New York: John Wiley and Sons.
     Angers, C. (1984). Large sample sizes for the estimation of multinomial frequencies
     from simulation studies. Simulation, 10, 175-178.
     Ardisia, c., Venti, G., Colozza, M.A., Breschi, c., Porfirio, B. , Davis, S., Tonato, M.,
     Donti, E. (1993). Expression of aphidicolin-induced fragile sites in lymphocytes of
     patients with breast cancer. Cancer Genet Cytogenet, 67, 113-116.
     Bakir, M. A., Byrne, M. D. (1994). An application of the multi-stage Monte Carlo
     optimization algorithm to aggregate production planning. International Journal of
     Production Economics, 35, 207-213 .
     Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975). Discrete Multivariate
     Analysis: Theory and Practice. Cambridge, MA, The MIT Press.
     Bohn, U., Dahm, P. F., McAllister, B. F., Greenbaum, I. F. (1995). Identifying
     chromosomal fragile sites from individuals: a multinomial statistical model. Hum
     Genet, 95, 249-256.
     Cochran, W. G. (1963). Sampling Techniques (2nd ed.), New York: 10lm Wiley.
     Cressie, N., Read, T. R. C. (1984). Multinomial goodness-of-fit tests. Journal of the
     Royal Statistical Society Series B 46,440-464.
     Cressie, N., Read, T. R. C. (1988) . Goodness-of-Fit Statistics for Discrete
     Multivariate Data, New York: Springer-Verlag.
     De Braekeleer, M. (1987). Fragile sites and chromosomal structure rearrangements in
     human leukemia and cancer. Anticancer Res., 7,417-422.
     De Braekeleer, M. (1989). Fragile sites and statistics. Hum Genet, 84, 103.
     De Braekeleer, M., Smith, B. (1988). Two methods for measuring the nonrandomness
     of chromosome abnormalities. Ann hum Genet 52 , 63-67.
     Ethier, S. N. (1982 ). Testing for favorable numbers on a roulette wheel. Journal of the American Statistical Association, 77, 660-665.
     Fienberg, S. E. (1980). The Analysis of Cross-Classified Categorical Data (2nd ed.).
     Cambridge, MA, the MIT Press.
     Fitzpatrick, S., Scott, A. (1987). Quick simultaneous confidence intervals for
     multinomial proportions. Journal of the American Statistical Association ., 82, 875-
     878.
     Freeman, D. H. (1987). Applied Categorical Data Analysis. New York, Marcel
     Dekker.
     Fuchs, c., Kenett, R. (1980). A test for detecting outlying cells in the multinomial
     distribution and two-way contingency tables. Journal of the American Statistical
     Association, 75, 395-398.
     Glaz, J., Johnson, B. (1984). Probability for multivariate distributions with
     dependence structures. Journal of the American Statistical Association, 79, 436-441.
     Gold, R. Z. (1963). Tests auxiliary to %2 tests in a Markov chain. Ann. Math. Statist.,
     34, 56-74.
     Goodman, L. A. (1965). On simultaneous confidence intervals for multinomial
     proportions. Technometrics, 7,247-254.
     Haberman, S. J. (1974) . The Analysis of Frequency Data. Chicago, University of
     Chicago Press.
     Hecht, F., Glover, T. W. (1984). Cancer chromosome breakpoints and common fragile sites induced by aphidicolin. Cancer Genet Cytogenet., 13, 185-188.
     Hecht, F., Sutherland, G. R. (1984). Fragile sites and cancer breakpoints. Cancer
     Genet Cytogenet, 12,179-181.
     Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of
     significance. Biometrika, 75,800-802.
     Holm, S. (1979). A simple sequentially rejective multiple test procedure.
     Scandinavian Journal of Statistics, 6, 65-70.
     Hurtubise, R. (1969). Sample sizes and confidence intervals associated with a Monte
     Carlo simulation model possessing a multinomial output. Simulation, 12, 71-77.
     ISCN. (1981). An international system for human cytogenetic nomenclature?high
     resolution banding. Cytogenet Cell Genet, 31, 1-23.
     JOMson, N. L., Kotz, S. (1970).Continuous Univariate Distributions-2. Houghton
     Mifflin, Boston.
     Jordan, D. K. , Bums, T. W., Divelbiss, J. E., Woolson, R. F., Patil, S. R. (1990) .
     Variability in expression of COnU1lOJ1 fragile sites: in search of a new criterion. Hum Genet, 85,462-466.
     Jowett, G. H. (1963). The relationship between the binomial and F distribution.
     Statistician, 13,55-57.
     Koehler, K., Larntz, K. (1980). An empirical investigation of goodness-of-fit statistics
     for sparse multinomials. Journal of the American Statistical Association, 75,336-344.
     Le Beau, M. M. (1986). Chromosomal fragile sites and cancer-specific· .
     rearrangements. Blood, 67, 849-858.
     Le Beau, M. M., Rowley, J. D. (1984). Heritable fragile sites and cancer. Nature, 308,
     607-608.
     Levin, B. (1981). A representation for multinomial cumulative distribution functions.
     The Annals of Statistics, 9,1123-1126.
     Mariani, T. (1989a). Fragile sites and statistics. Hum Genet, 81, 319-322.
     Mariani, T. (1989b). Reply to letter by M. De Braekeleer. Hum Genet, 84, 104.
     Mehta, C. R., Patel, N. R. , Senchaudhuri, P. (1988). Importance sampling for
     estimating exact probabilities in permutational inference. Journal of the American
     Statistical Association, 83,999-1005.
     Miller, R. G., Jr. (1977). Developments in mUltiple comparisons 1966-l976 . .Tournai
     of the American Statistical Association, 72, 779-788.
     Miller, R. G., Jr. (1981). Simultaneous Statistical Inference (2nd ed.). New York:
     Springer-Verlag.
     Nelson, L. S. (1995). The usefulness of Monte Carlo tests. Journal of Quality
     Technology, 27, 387-389.
     Quesenberry, C. P., Hurst D. C. (1964). Simultaneous confidence intervals for
     multinomial proportions. Technometrics, 6, 191-195.
     Roy, S. N. (1953). On a heuristic method of test construction and its use in
     multivariate analysis. Ann. Math. Stat., 24, 220-238.
     Seber, G. A. (1977). Linear regression analysis. Wiley, New York.
     Sison, C. P., Glaz, 1. (1995). Simultaneous confidence intervals and sample size
     determination for multinomial proportions. Journal of the American Statistical
     Association, 90, 366-369.
     Smith, CAB. (1986). Chi:`squared tests with small numbers. Ann hum Genet, 50, 163-
     167.
     Sobol, J. M. (1974). The Monte Carlo Method. The University of Chicago Press.
     Sutherland, G. R., Ledbetter, D. H. (1989). Report of the committee on cytogenetic
     markers. Tenth International Workshop on Human Gene Mapping. Cytogenet Cell
     Genet, 51, 452-458.
     Tai,J. J., Hou, C-D., Wang-Wuu, S., Wang, C-H., Leu, S-Y., Wuu, K-D. (1993). A
     method for testing the nonrandonmess of chromosomal breakpoints. Cytogenet Cell
     Genet, 63,147-150.
     Tarone, R. E. (1989). Testing for nonrandol111less of events in sparse data situations.
     Ann hum Genet, 53,381-387.
     Thompson, E. A. (1994). Monte Carlo likelihood in genetic mapping. Statistical
     Science, 9, 355-366.
     Thompson, S. K. (1987). Sample size for estimating multinomial proportions. The
     American Statistician, 41 , 42-46.
     Tortora, R. D. (1978) . A note on sample size estimation for multinomial populations.
     The American Statistician, 32, 100-102.
     Troendle, J. F. (1995). A stepwise resampling method of multiple hypothesis testing.
     Journal of the American Statistical Association, 90, 370-378.
     Vasarhelyi, K., Friedman, J. M. (1989). Analyzing rearrangement between breakpoint
     distributions by means of binomial confidence intervals. Ann hum Genet, 3,375-380.
     Wang, C-H. , Leu, S- Y., Tai, J. J., Wuu, K-D., Wang-Wuu, S. (1992). Chromosomal
     fragile sites expression in lymphocytes of patients ,,with colorectal carcinoma and of
     healthy controls. Ms. Submitted for publication.
     Zar, J. H. (1984). Biostatistical Analysis. Prentice-Hall, Englewood Cliffs.		zh_TW