메뉴 건너뛰기




Volumn 34, Issue 2, 2006, Pages 878-902

An iterative procedure for general probability measures to obtain I-projections onto intersections of convex sets

Author keywords

Algorithm; Convergence; Convex sets; Fenchel duality; Functions; I projection; Inequality constraints; Stochastic order

Indexed keywords


EID: 33746185539     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000056     Document Type: Article
Times cited : (13)

References (28)
  • 2
    • 33746180238 scopus 로고
    • A general duality approach to I-projections
    • MR1364994
    • BHATTACHARYA, B. and DYKSTRA, R. (1995). A general duality approach to I-projections. J. Statist. Plann. Inference 47 203-216. MR1364994
    • (1995) J. Statist. Plann. Inference , vol.47 , pp. 203-216
    • Bhattacharya, B.1    Dykstra, R.2
  • 3
    • 9844235918 scopus 로고    scopus 로고
    • A Fenchel duality aspect of iterative I-projection procedures
    • MR1482366
    • BHATTACHARYA, B. and DYKSTRA, R. (1997). A Fenchel duality aspect of iterative I-projection procedures. Ann. Inst. Statist. Math. 49 435-446. MR1482366
    • (1997) Ann. Inst. Statist. Math. , vol.49 , pp. 435-446
    • Bhattacharya, B.1    Dykstra, R.2
  • 6
    • 0000546609 scopus 로고
    • I-divergence geometry of probability distributions and minimization problems
    • MR0365798
    • CSISZÁR, I. (1975). I-divergence geometry of probability distributions and minimization problems. Ann. Probab. 3 146-158. MR0365798
    • (1975) Ann. Probab. , vol.3 , pp. 146-158
    • Csiszár, I.1
  • 7
    • 0010159449 scopus 로고
    • A geometric interpretation of Darroch and Ratcliff's generalized iterative scaling
    • MR1015161
    • CSISZÁR, I. (1989). A geometric interpretation of Darroch and Ratcliff's generalized iterative scaling. Ann. Statist. 17 1409-1413. MR1015161
    • (1989) Ann. Statist. , vol.17 , pp. 1409-1413
    • Csiszár, I.1
  • 8
    • 0001573124 scopus 로고
    • Generalized iterative scaling for loglinear models
    • MR0345337
    • DARROCH, J. N. and RATCLIFF, D. (1972). Generalized iterative scaling for loglinear models. Ann. Math. Statist. 43 1470-1480. MR0345337
    • (1972) Ann. Math. Statist. , vol.43 , pp. 1470-1480
    • Darroch, J.N.1    Ratcliff, D.2
  • 9
    • 0000695960 scopus 로고
    • On a least squares adjustment of a sampled frequency table when the expected marginal totals are known
    • MR0003527
    • DEMING, W. E. and STEPHAN, F. F. (1940). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Statist. 11 427-444. MR0003527
    • (1940) Ann. Math. Statist. , vol.11 , pp. 427-444
    • Deming, W.E.1    Stephan, F.F.2
  • 10
    • 0010015340 scopus 로고
    • An iterative procedure for obtaining I-projections onto the intersection of convex sets
    • MR0799432
    • DYKSTRA, R. (1985). An iterative procedure for obtaining I-projections onto the intersection of convex sets. Ann. Probab. 13 975-984. MR0799432
    • (1985) Ann. Probab. , vol.13 , pp. 975-984
    • Dykstra, R.1
  • 11
    • 0001442350 scopus 로고
    • Duality of I-projections and maximum likelihood estimation for log-linear models under cone constraints
    • MR0971385
    • DYKSTRA, R. and LEMKE, J. H. (1988). Duality of I-projections and maximum likelihood estimation for log-linear models under cone constraints. J. Amer. Statist. Assoc. 83 546-554. MR0971385
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 546-554
    • Dykstra, R.1    Lemke, J.H.2
  • 12
    • 0001373576 scopus 로고
    • Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables
    • MR0150880
    • GOOD, I. J. (1963). Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables. Ann. Math. Statist. 34 911-934. MR0150880
    • (1963) Ann. Math. Statist. , vol.34 , pp. 911-934
    • Good, I.J.1
  • 14
    • 0005746898 scopus 로고
    • Adjustment by minimum discriminant information
    • MR0751286
    • HABERMAN, S. J. (1984). Adjustment by minimum discriminant information. Ann. Statist. 12 971-988. MR0751286
    • (1984) Ann. Statist. , vol.12 , pp. 971-988
    • Haberman, S.J.1
  • 15
    • 0014256178 scopus 로고
    • Contingency tables with given marginals
    • MR0229329
    • IRELAND, C. T. and KULLBACK, S. (1968). Contingency tables with given marginals. Biometrika 55 179-188. MR0229329
    • (1968) Biometrika , vol.55 , pp. 179-188
    • Ireland, C.T.1    Kullback, S.2
  • 16
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • MR0087305
    • JAYNES, E. T. (1957). Information theory and statistical mechanics. Phys. Rev. (2) 106 620-630. MR0087305
    • (1957) Phys. Rev. (2) , vol.106 , pp. 620-630
    • Jaynes, E.T.1
  • 18
    • 0039977168 scopus 로고
    • Telefoonverkeersrekening
    • KRUITHOF, R. (1937). Telefoonverkeersrekening. De Ingenieur 52 E15-E25.
    • (1937) De Ingenieur , vol.52
    • Kruithof, R.1
  • 20
    • 0039607518 scopus 로고
    • Probability densities with given marginals
    • MR0229330
    • KULLBACK, S. (1968). Probability densities with given marginals. Ann. Math. Statist. 39 1236-1243. MR0229330
    • (1968) Ann. Math. Statist. , vol.39 , pp. 1236-1243
    • Kullback, S.1
  • 21
    • 33746180240 scopus 로고
    • On the existence of f-projections
    • (I. Csiszár and P. Elias, eds.). North-Holland, Amsterdam. MR0459930
    • LIESE, F. (1977). On the existence of f-projections. In Topics in Information Theory (I. Csiszár and P. Elias, eds.) 431-446. North-Holland, Amsterdam. MR0459930
    • (1977) Topics in Information Theory , pp. 431-446
    • Liese, F.1
  • 25
    • 21844498858 scopus 로고
    • Convergence of the iterative proportional fitting procedure
    • MR1353500
    • RÜSCHENDORF, L. (1995). Convergence of the iterative proportional fitting procedure. Ann. Statist. 23 1160-1174. MR1353500
    • (1995) Ann. Statist. , vol.23 , pp. 1160-1174
    • Rüschendorf, L.1
  • 26
    • 38249003518 scopus 로고
    • Note on the schrodinger equation and I-projections
    • MR1237783
    • RÜSCHENDORF, L. and THOMSEN, W. (1993). Note on the Schrodinger equation and I-projections. Statist. Probab. Lett. 17 369-375. MR1237783
    • (1993) Statist. Probab. Lett. , vol.17 , pp. 369-375
    • Rüschendorf, L.1    Thomsen, W.2
  • 27
    • 0009909847 scopus 로고
    • On the probability of large deviations of random magnitudes
    • MR0088087
    • SANOV, I. N. (1957). On the probability of large deviations of random magnitudes. Mat. Sb. N.S. 42 11-44. MR0088087
    • (1957) Mat. Sb. N.S. , vol.42 , pp. 11-44
    • Sanov, I.N.1
  • 28
    • 0642273495 scopus 로고
    • On Dykstra's iterative fitting procedure
    • MR1062075
    • WINKLER, W. (1990). On Dykstra's iterative fitting procedure. Ann. Probab. 18 1410-1415. MR1062075
    • (1990) Ann. Probab. , vol.18 , pp. 1410-1415
    • Winkler, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.