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Volumn 54, Issue 2, 1996, Pages 201-227

Duality between multiple testing and selecting

Author keywords

Admissibility of subset selection procedures; Least favorable parameter configuration; Multiple hypotheses testing; Step down selection procedure; Step up selection procedure; Subset selection

Indexed keywords


EID: 0030590307     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-3758(95)00168-9     Document Type: Article
Times cited : (12)

References (52)
  • 1
    • 0000691392 scopus 로고
    • Indifference-zone ranking and selection: Confidence intervals for true achieved P(CD)
    • Anderson, P.O., T.A. Bishop and E.J. Dudewicz (1977). Indifference-zone ranking and selection: confidence intervals for true achieved P(CD). Comm. Statist. Theory Methods 6, 1121-1132.
    • (1977) Comm. Statist. Theory Methods , vol.6 , pp. 1121-1132
    • Anderson, P.O.1    Bishop, T.A.2    Dudewicz, E.J.3
  • 2
    • 0002426110 scopus 로고
    • A single-sample multiple decision procedure for ranking normal populations with known variances
    • Bechhofer, R.E. (1954). A single-sample multiple decision procedure for ranking normal populations with known variances. Ann. Math. Statist. 25, 16-39.
    • (1954) Ann. Math. Statist. , vol.25 , pp. 16-39
    • Bechhofer, R.E.1
  • 3
    • 0021653101 scopus 로고
    • Selection and ranking procedures - Some personal reminiscences, and thoughts about its past, present, and future
    • Bechhofer, R.E. (1985). Selection and ranking procedures - some personal reminiscences, and thoughts about its past, present, and future. Amer. J. Math. Management Sci. 5, 201-233.
    • (1985) Amer. J. Math. Management Sci. , vol.5 , pp. 201-233
    • Bechhofer, R.E.1
  • 5
    • 84985532033 scopus 로고
    • Multiple comparisons and selection
    • Bofinger, E. (1983). Multiple comparisons and selection. Austral. J. Statist. 25, 198-207.
    • (1983) Austral. J. Statist. , vol.25 , pp. 198-207
    • Bofinger, E.1
  • 6
    • 84985572108 scopus 로고
    • Step down procedures for comparisons with a control
    • Bofinger, E. (1987). Step down procedures for comparisons with a control. Austral. J. Statist. 29, 348-364.
    • (1987) Austral. J. Statist. , vol.29 , pp. 348-364
    • Bofinger, E.1
  • 7
    • 0001158897 scopus 로고
    • Least significant spacing for 'one versus the rest' normal populations
    • Bofinger, E. (1988). Least significant spacing for 'one versus the rest' normal populations. Comm. Statist. Theory Methods 17, 1697-1716.
    • (1988) Comm. Statist. Theory Methods , vol.17 , pp. 1697-1716
    • Bofinger, E.1
  • 8
    • 84990530724 scopus 로고
    • Should we estimate the probability of correct selection?
    • Bofinger, E. (1994). Should we estimate the probability of correct selection? Austral. J. Statist. 36, 59-66.
    • (1994) Austral. J. Statist. , vol.36 , pp. 59-66
    • Bofinger, E.1
  • 9
    • 84963193734 scopus 로고
    • On sequentially rejective subset selection procedures
    • Broström, G. (1981). On sequentially rejective subset selection procedures. Comm. Statist. Theory Methods 10, 203-221.
    • (1981) Comm. Statist. Theory Methods , vol.10 , pp. 203-221
    • Broström, G.1
  • 10
    • 84972521266 scopus 로고
    • An alternative to student's t-test for problems with indifference zones
    • Brown, L.D. and H. Sackrowitz (1984). An alternative to Student's t-test for problems with indifference zones. Ann. Statist. 12, 451-469.
    • (1984) Ann. Statist. , vol.12 , pp. 451-469
    • Brown, L.D.1    Sackrowitz, H.2
  • 11
    • 84917786962 scopus 로고
    • An evaluation of ten multiple comparison procedures by Monte Carlo techniques
    • Carmer, S.G. and M.R. Swanson (1973). An evaluation of ten multiple comparison procedures by Monte Carlo techniques. J. Amer. Statist. Assoc. 68, 66-74.
    • (1973) J. Amer. Statist. Assoc. , vol.68 , pp. 66-74
    • Carmer, S.G.1    Swanson, M.R.2
  • 12
    • 0001599065 scopus 로고
    • The power function of range and studentised range tests in normal samples
    • David, H.A., P.A. Lachenbruch and H.P. Brandis (1972). The power function of range and studentised range tests in normal samples. Biometrika 59, 161-168.
    • (1972) Biometrika , vol.59 , pp. 161-168
    • David, H.A.1    Lachenbruch, P.A.2    Brandis, H.P.3
  • 14
    • 0002938647 scopus 로고
    • On the modified S-method and directional errors
    • Finner, H. (1990). On the modified S-method and directional errors. Comm. Statist. Theory Methods 19, 41-53.
    • (1990) Comm. Statist. Theory Methods , vol.19 , pp. 41-53
    • Finner, H.1
  • 15
    • 38149144359 scopus 로고
    • Closed subset selection procedures for selecting good populations
    • Finner, H. and G. Giani (1994). Closed subset selection procedures for selecting good populations. J. Statist. Plann. Inference 38, 179-199.
    • (1994) J. Statist. Plann. Inference , vol.38 , pp. 179-199
    • Finner, H.1    Giani, G.2
  • 17
    • 0001276589 scopus 로고
    • On the limit behaviour of the joint distribution function of order statistics
    • Finner, H. and M. Roters (1994). On the limit behaviour of the joint distribution function of order statistics. Ann. Inst. Statist. Math. 46, 343-349.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 343-349
    • Finner, H.1    Roters, M.2
  • 18
    • 0000279774 scopus 로고
    • Simultaneous test procedures - Some theory of multiple comparisons
    • Gabriel, K.R. (1969). Simultaneous test procedures - some theory of multiple comparisons. Ann. Math. Statist. 40, 224-250.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 224-250
    • Gabriel, K.R.1
  • 19
    • 0002445912 scopus 로고
    • Some general results on least favorable parameter configurations with special reference to equivalence testing and the range statistic
    • Giani, G. and H. Finner (1991). Some general results on least favorable parameter configurations with special reference to equivalence testing and the range statistic. J. Statist. Plann. Inference 28, 33-47.
    • (1991) J. Statist. Plann. Inference , vol.28 , pp. 33-47
    • Giani, G.1    Finner, H.2
  • 20
    • 21344496924 scopus 로고
    • Testing and selecting for equivalence with respect to a control
    • Giani, G. and K. Strassburger (1994). Testing and selecting for equivalence with respect to a control. J. Amer. Statist. Assoc. 89, 320-329.
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 320-329
    • Giani, G.1    Strassburger, K.2
  • 22
    • 0003771532 scopus 로고
    • Ph.D. Thesis (Mimeo Ser. No. 150). Inst. of Statist., Univ. of North Carolina, Chapel Hill
    • Gupta, S.S. (1956). On a decision rule for a problem in ranking means. Ph.D. Thesis (Mimeo Ser. No. 150). Inst. of Statist., Univ. of North Carolina, Chapel Hill.
    • (1956) On a Decision Rule for a Problem in Ranking Means
    • Gupta, S.S.1
  • 23
    • 0001186451 scopus 로고
    • On some multiple decision (selection and ranking) rules
    • Gupta, S.S. (1965). On some multiple decision (selection and ranking) rules. Technometrics 7, 225-245.
    • (1965) Technometrics , vol.7 , pp. 225-245
    • Gupta, S.S.1
  • 24
    • 84963474740 scopus 로고
    • On lower confidence bounds for PCS in truncated location parameter models
    • Gupta, S.S., L.Y. Leu and T. Liang (1990). On lower confidence bounds for PCS in truncated location parameter models. Comm. Statist. Theory Methods 19, 527-546.
    • (1990) Comm. Statist. Theory Methods , vol.19 , pp. 527-546
    • Gupta, S.S.1    Leu, L.Y.2    Liang, T.3
  • 26
    • 0000495105 scopus 로고
    • Is the selected population the best?
    • Gutmann, S. and Z. Maymin (1987). Is the selected population the best? Ann. Statist. 15, 456-461.
    • (1987) Ann. Statist. , vol.15 , pp. 456-461
    • Gutmann, S.1    Maymin, Z.2
  • 28
    • 0000789312 scopus 로고
    • Simultaneous confidence intervals for all distances with the 'best'
    • Hsu, J.C. (1981). Simultaneous confidence intervals for all distances with the 'best'. Ann. Statist. 9, 1026-1034.
    • (1981) Ann. Statist. , vol.9 , pp. 1026-1034
    • Hsu, J.C.1
  • 29
    • 0000210329 scopus 로고
    • Constrained simultaneous confidence intervals for multiple comparisons with the best
    • Hsu, J.C. (1984). Constrained simultaneous confidence intervals for multiple comparisons with the best. Ann. Statist. 12, 1136-1144.
    • (1984) Ann. Statist. , vol.12 , pp. 1136-1144
    • Hsu, J.C.1
  • 30
    • 0000026883 scopus 로고
    • A method of unconstrained multiple comparisons with the best
    • Hsu, J.C. (1985). A method of unconstrained multiple comparisons with the best. Comm. Statist. Theory Methods 14, 2009-2028.
    • (1985) Comm. Statist. Theory Methods , vol.14 , pp. 2009-2028
    • Hsu, J.C.1
  • 31
    • 38249007810 scopus 로고
    • Stepwise multiple comparisons with the best
    • Hsu, J.C. (1992). Stepwise multiple comparisons with the best. J. Statist. Plann. Inference 33, 197-204.
    • (1992) J. Statist. Plann. Inference , vol.33 , pp. 197-204
    • Hsu, J.C.1
  • 32
    • 0002612264 scopus 로고
    • A lower confidence bound on the probability of a correct selection
    • Kim, W.-C. (1986). A lower confidence bound on the probability of a correct selection. J. Amer. Statist. Assoc. 81, 1012-1017.
    • (1986) J. Amer. Statist. Assoc. , vol.81 , pp. 1012-1017
    • Kim, W.-C.1
  • 33
    • 0000555447 scopus 로고
    • A new procedure for selecting good populations
    • Lam, K. (1986). A new procedure for selecting good populations. Biometrika 73, 201-206.
    • (1986) Biometrika , vol.73 , pp. 201-206
    • Lam, K.1
  • 34
    • 0001799563 scopus 로고
    • A theory of some multiple decision problems - part I
    • Lehmann, E.L. (1957). A theory of some multiple decision problems - part I. Ann. Math. Statist. 28, 547-572.
    • (1957) Ann. Math. Statist. , vol.28 , pp. 547-572
    • Lehmann, E.L.1
  • 35
    • 0017146303 scopus 로고
    • On closed testing procedures with special reference to ordered analysis of variance
    • Marcus, R., E. Peritz and K.R. Gabriel (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63, 655-660.
    • (1976) Biometrika , vol.63 , pp. 655-660
    • Marcus, R.1    Peritz, E.2    Gabriel, K.R.3
  • 36
    • 84988080190 scopus 로고
    • Testing retrospective hypotheses
    • Mayman, Z. and S. Gutmann (1992). Testing retrospective hypotheses. Canad. J. Statist. 20, 335-345.
    • (1992) Canad. J. Statist. , vol.20 , pp. 335-345
    • Mayman, Z.1    Gutmann, S.2
  • 37
    • 0001641846 scopus 로고
    • Identification and selection procedures based on tests
    • Miescke, K.J. (1979). Identification and selection procedures based on tests. Ann. Statist. 7, 207-219.
    • (1979) Ann. Statist. , vol.7 , pp. 207-219
    • Miescke, K.J.1
  • 39
    • 84963223395 scopus 로고
    • Some selection rules for comparing p processes with a standard
    • Naik, U.D. (1975). Some selection rules for comparing p processes with a standard. Comm. Statist. 4, 519-535.
    • (1975) Comm. Statist. , vol.4 , pp. 519-535
    • Naik, U.D.1
  • 40
    • 0000127646 scopus 로고
    • Some subset selection problems
    • Naik, U.D. (1977). Some subset selection problems. Comm. Statist. Theory Methods 6, 955-966.
    • (1977) Comm. Statist. Theory Methods , vol.6 , pp. 955-966
    • Naik, U.D.1
  • 41
    • 0011495306 scopus 로고
    • Procedures with lower expected subset size than that of gupta's subset selection procedure for three normal populations
    • Preez, J.P. Du, J.W.H. Swanepoel, J.H. Venter and P.N. Somerville (1985a). Procedures with lower expected subset size than that of Gupta's subset selection procedure for three normal populations. South African Statist. J. 19, 115-125.
    • (1985) South African Statist. J. , vol.19 , pp. 115-125
    • Preez, J.P.1    Du2    Swanepoel, J.W.H.3    Venter, J.H.4    Somerville, P.N.5
  • 42
    • 0011456285 scopus 로고
    • Some properties of Somerville's multiple range subset selection procedure for three populations
    • Preez, J.P. Du, J.W.H. Swanepoel, J.H. Venter and P.N. Somerville (1985b). Some properties of Somerville's multiple range subset selection procedure for three populations. South African Statist. J. 19, 45-72.
    • (1985) South African Statist. J. , vol.19 , pp. 45-72
    • Preez, J.P.1    Du2    Swanepoel, J.W.H.3    Venter, J.H.4    Somerville, P.N.5
  • 43
    • 0000485147 scopus 로고
    • On logarithmic concave measures and functions
    • Prekopa, A. (1973). On logarithmic concave measures and functions. Acta Sci. Math. (Szeged) 36, 335-343.
    • (1973) Acta Sci. Math. (Szeged) , vol.36 , pp. 335-343
    • Prekopa, A.1
  • 44
    • 0001618721 scopus 로고
    • A sequentially rejective test procedure based on a modified bonferroni inequality
    • Rom, D.M. (1990). A sequentially rejective test procedure based on a modified Bonferroni inequality. Biometrika 77, 663-665.
    • (1990) Biometrika , vol.77 , pp. 663-665
    • Rom, D.M.1
  • 45
    • 0011403776 scopus 로고
    • A multiple range subset selection procedure
    • Somerville, P.N. (1984). A multiple range subset selection procedure. J. Statist. Comput. Simulation 19, 215-226.
    • (1984) J. Statist. Comput. Simulation , vol.19 , pp. 215-226
    • Somerville, P.N.1
  • 46
    • 0011497490 scopus 로고
    • A new subset selection method for normal populations
    • Somerville. P.N. (1985a). A new subset selection method for normal populations. J. Statist. Comput. Simulation 22, 27-50.
    • (1985) J. Statist. Comput. Simulation , vol.22 , pp. 27-50
    • Somerville, P.N.1
  • 48
    • 0021648741 scopus 로고
    • On the geometry of some subset selection procedures
    • Somerville, P.N. (1986). On the geometry of some subset selection procedures. Amer. J. Math. Management Sci. 6, 169-184.
    • (1986) Amer. J. Math. Management Sci. , vol.6 , pp. 169-184
    • Somerville, P.N.1
  • 49
    • 0041611570 scopus 로고
    • Vollständigkeitssätze für multiple testprobleme
    • P. Bauer, G. Hommel and E. Sonnemann, Eds., Springer, Berlin
    • Sonnemann, E. and H. Finner (1988). Vollständigkeitssätze für multiple Testprobleme (Complete class theorems for testing multiple hypotheses). In: P. Bauer, G. Hommel and E. Sonnemann, Eds., Multiple Hypothesenprüfung - Multiple Hypotheses Testing. Springer, Berlin, 121-135.
    • (1988) Multiple Hypothesenprüfung - Multiple Hypotheses Testing , pp. 121-135
    • Sonnemann, E.1    Finner, H.2
  • 50
    • 0002427627 scopus 로고
    • On confidence sets in multiple comparisons
    • S.S. Gupta and J.O. Berger, Eds., Academic Press, New York
    • Stefansson, G., W.-C. Kim and J.C. Hsu (1988). On confidence sets in multiple comparisons. In: S.S. Gupta and J.O. Berger, Eds., Statistical Decision Theory and related Topics, Vol. IV. Academic Press, New York, 89-104.
    • (1988) Statistical Decision Theory and Related Topics , vol.4 , pp. 89-104
    • Stefansson, G.1    Kim, W.-C.2    Hsu, J.C.3
  • 51
    • 0010525634 scopus 로고
    • Stepwise multiple comparison procedures
    • Welsch, R.E. (1977). Stepwise multiple comparison procedures. J. Amer. Statist. Assoc. 72, 566-575.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 566-575
    • Welsch, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.