메뉴 건너뛰기




Volumn 18, Issue 5, 2008, Pages 1910-1943

Linear and quadratic functionals of random hazard rates: An asymptotic analysis

Author keywords

Asymptotics; Bayesian nonparametrics; Central limit theorem; Completely random measure; Multiple Wiener It integral; Path variance; Random hazard rate; Survival analysis

Indexed keywords


EID: 63049102708     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/07-AAP509     Document Type: Article
Times cited : (18)

References (50)
  • 1
    • 63049095564 scopus 로고    scopus 로고
    • AALEN, O. (1978). Nonparametric inference for a family of counting processes. Ann. Statist. 6 701-726. MR491547
    • AALEN, O. (1978). Nonparametric inference for a family of counting processes. Ann. Statist. 6 701-726. MR491547
  • 2
    • 0035648379 scopus 로고    scopus 로고
    • Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics
    • MR1841412
    • BARNDORFF-NIELSEN, O. E. and SHEPHARD, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 167-241. MR1841412
    • (2001) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.63 , pp. 167-241
    • BARNDORFF-NIELSEN, O.E.1    SHEPHARD, N.2
  • 3
    • 0033333437 scopus 로고    scopus 로고
    • Generalized gamma measures and shot-noise Cox processes
    • MR1747450
    • BRIX, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. in Appl. Probab. 31 929-953. MR1747450
    • (1999) Adv. in Appl. Probab , vol.31 , pp. 929-953
    • BRIX, A.1
  • 4
    • 0034287160 scopus 로고    scopus 로고
    • Some new results for Dirichlet priors
    • MR1805789
    • CIFARELLI, D. M. and MELILLI, E. (2000). Some new results for Dirichlet priors. Ann. Statist. 28 1390-1413. MR1805789
    • (2000) Ann. Statist , vol.28 , pp. 1390-1413
    • CIFARELLI, D.M.1    MELILLI, E.2
  • 5
    • 0000771631 scopus 로고
    • Distribution functions of means of a Dirichlet process
    • MR1041402
    • CIFARELLI, D. M. and REGAZZINI, E. (1990). Distribution functions of means of a Dirichlet process. Ann. Statist. 18 429-442. MR1041402
    • (1990) Ann. Statist , vol.18 , pp. 429-442
    • CIFARELLI, D.M.1    REGAZZINI, E.2
  • 6
    • 33847351562 scopus 로고    scopus 로고
    • Bayesian survival analysis in proportional hazard models with logistic relative risk
    • MR2325252
    • DE BLASI, P. and HJORT, N. L. (2007). Bayesian survival analysis in proportional hazard models with logistic relative risk. Scand. J. Statist. 34 229-257. MR2325252
    • (2007) Scand. J. Statist , vol.34 , pp. 229-257
    • DE BLASI, P.1    HJORT, N.L.2
  • 7
    • 84869261128 scopus 로고    scopus 로고
    • Asymptotics for posterior hazards. Technical report
    • Submitted
    • DE BLASI, P., PECCATI, G. and PRÜNSTER, I. (2007). Asymptotics for posterior hazards. Technical report. Submitted.
    • (2007)
    • DE BLASI, P.1    PECCATI, G.2    PRÜNSTER, I.3
  • 8
    • 63049098202 scopus 로고    scopus 로고
    • DALEY, D. J. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York. MR950166
    • DALEY, D. J. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York. MR950166
  • 9
    • 31344433208 scopus 로고    scopus 로고
    • On quadratic functionals of the Brownian sheet and related processes
    • MR2199561
    • DEHEUVELS, P., PECCATI, G. and YOR, M. (2006). On quadratic functionals of the Brownian sheet and related processes. Stochastic Process. Appl. 116 493-538. MR2199561
    • (2006) Stochastic Process. Appl , vol.116 , pp. 493-538
    • DEHEUVELS, P.1    PECCATI, G.2    YOR, M.3
  • 10
    • 0000111818 scopus 로고
    • Tailfree and neutral random probabilities and their posterior distributions
    • MR0373081
    • DOKSUM, K. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 183-201. MR0373081
    • (1974) Ann. Probab , vol.2 , pp. 183-201
    • DOKSUM, K.1
  • 11
    • 26444439199 scopus 로고    scopus 로고
    • Consistency of Dykstra-Laud priors
    • MR2028910
    • DRǍGHICI, L. and RAMAMOORTHI, R. V (2003). Consistency of Dykstra-Laud priors. Sankhyā 65 464-481. MR2028910
    • (2003) Sankhyā , vol.65 , pp. 464-481
    • DRǍGHICI, L.1    RAMAMOORTHI, R.V.2
  • 12
    • 63049091635 scopus 로고    scopus 로고
    • DYKSTRA, R. L. and LAUD, P. (1981). A Bayesian nonparametric approach to reliability. Ann. Statist. 9 356-367. MR606619
    • DYKSTRA, R. L. and LAUD, P. (1981). A Bayesian nonparametric approach to reliability. Ann. Statist. 9 356-367. MR606619
  • 13
    • 3843126281 scopus 로고    scopus 로고
    • Exponential functionals and means of neutral-to-the-right priors
    • MR2024758
    • EPIFANI, I., LIJOI, A. and PRÜNSTER, I. (2003). Exponential functionals and means of neutral-to-the-right priors. Biometrika 90 791-808. MR2024758
    • (2003) Biometrika , vol.90 , pp. 791-808
    • EPIFANI, I.1    LIJOI, A.2    PRÜNSTER, I.3
  • 14
    • 0000780135 scopus 로고
    • Prior distributions on spaces of probability measures
    • MR0438568
    • FERGUSON, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2 615-629. MR0438568
    • (1974) Ann. Statist , vol.2 , pp. 615-629
    • FERGUSON, T.S.1
  • 15
    • 63049131761 scopus 로고    scopus 로고
    • FERGUSON, T. S. and PHADIA, E. G. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 1163-186. MR515691
    • FERGUSON, T. S. and PHADIA, E. G. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 1163-186. MR515691
  • 16
    • 63049122714 scopus 로고    scopus 로고
    • GHOSH, J. K. and RAMAMOORTHI, R. V. (2003). Bayesian Nonparametrics. Springer, New York. MR1992245
    • GHOSH, J. K. and RAMAMOORTHI, R. V. (2003). Bayesian Nonparametrics. Springer, New York. MR1992245
  • 17
    • 0001241617 scopus 로고
    • Nonparametric Bayes estimators based on beta processes in models for life history data
    • MR1062708
    • HJORT, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294. MR1062708
    • (1990) Ann. Statist , vol.18 , pp. 1259-1294
    • HJORT, N.L.1
  • 18
    • 33746253028 scopus 로고    scopus 로고
    • A Bayes method for a monotone hazard rate via S-paths
    • MR2283394
    • HO, M.-W. (2006). A Bayes method for a monotone hazard rate via S-paths. Ann. Statist. 34 820-836. MR2283394
    • (2006) Ann. Statist , vol.34 , pp. 820-836
    • HO, M.-W.1
  • 19
    • 1842816362 scopus 로고    scopus 로고
    • Gibbs sampling methods for stick-breaking priors
    • MR1952729
    • ISHWARAN, H. and JAMES, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96 161-173. MR1952729
    • (2001) J. Amer. Statist. Assoc , vol.96 , pp. 161-173
    • ISHWARAN, H.1    JAMES, L.F.2
  • 20
    • 2142830935 scopus 로고    scopus 로고
    • Computational methods for multiplicative intensity models using weighted gamma processes: Proportional hazards, marked point processes, and panel count data
    • MR2054297
    • ISHWARAN, H. and JAMES, L. F. (2004). Computational methods for multiplicative intensity models using weighted gamma processes: Proportional hazards, marked point processes, and panel count data. J. Amer. Statist. Assoc. 99 175-190. MR2054297
    • (2004) J. Amer. Statist. Assoc , vol.99 , pp. 175-190
    • ISHWARAN, H.1    JAMES, L.F.2
  • 21
    • 0348146266 scopus 로고    scopus 로고
    • Bayesian calculus for gamma processes with applications to semiparametric intensity models
    • MR2016784
    • JAMES, L. F. (2003). Bayesian calculus for gamma processes with applications to semiparametric intensity models. Sankhyā 65 179-206. MR2016784
    • (2003) Sankhyā , vol.65 , pp. 179-206
    • JAMES, L.F.1
  • 22
    • 26444603040 scopus 로고    scopus 로고
    • JAMES, L. F. (2005). Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages. Ann. Statist. 33 1771-1799. MR2166562
    • JAMES, L. F. (2005). Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages. Ann. Statist. 33 1771-1799. MR2166562
  • 23
    • 33744827696 scopus 로고    scopus 로고
    • Poisson calculus for spatial neutral to the right processes
    • MR2275248
    • JAMES, L. F. (2006). Poisson calculus for spatial neutral to the right processes. Ann. Statist. 34 416-440. MR2275248
    • (2006) Ann. Statist , vol.34 , pp. 416-440
    • JAMES, L.F.1
  • 24
    • 63049089730 scopus 로고    scopus 로고
    • KALBFLEISCH, J. D. (1978). Non-parametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40 214-221. MR517442
    • KALBFLEISCH, J. D. (1978). Non-parametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40 214-221. MR517442
  • 25
    • 0033471036 scopus 로고    scopus 로고
    • Nonparametric Bayesian estimators for counting processes
    • MR1714717
    • KIM, Y. (1999). Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27 562-588. MR1714717
    • (1999) Ann. Statist , vol.27 , pp. 562-588
    • KIM, Y.1
  • 26
    • 0037688249 scopus 로고    scopus 로고
    • Bayesian analysis of proportional hazard models
    • MR1983539
    • KIM, Y. and LEE, J. (2003). Bayesian analysis of proportional hazard models. Ann. Statist. 31 493-511. MR1983539
    • (2003) Ann. Statist , vol.31 , pp. 493-511
    • KIM, Y.1    LEE, J.2
  • 27
    • 84969653882 scopus 로고
    • Completely random measures
    • MR0210185
    • KINGMAN, J. F. C. (1967). Completely random measures. Pacific J. Math. 21 59-78. MR0210185
    • (1967) Pacific J. Math , vol.21 , pp. 59-78
    • KINGMAN, J.F.C.1
  • 28
    • 63049111661 scopus 로고    scopus 로고
    • KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Studies in Probability 3. Oxford Univ. Press, New York. MR1207584
    • KINGMAN, J. F. C. (1993). Poisson Processes. Oxford Studies in Probability 3. Oxford Univ. Press, New York. MR1207584
  • 29
    • 84869248019 scopus 로고    scopus 로고
    • KWAPIEŃ, S. and WOYCZYŃSKI, W. A. (1992). Random Series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston, MA. MR1167198
    • KWAPIEŃ, S. and WOYCZYŃSKI, W. A. (1992). Random Series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston, MA. MR1167198
  • 30
    • 29144511286 scopus 로고    scopus 로고
    • Hierarchical mixture modeling with normalized inverse-Gaussian priors
    • MR2236441
    • LIJOI, A., MENA, R. H. and PRÜNSTER, I. (2005). Hierarchical mixture modeling with normalized inverse-Gaussian priors. J. Amer. Statist. Assoc. 100 1278-1291. MR2236441
    • (2005) J. Amer. Statist. Assoc , vol.100 , pp. 1278-1291
    • LIJOI, A.1    MENA, R.H.2    PRÜNSTER, I.3
  • 31
    • 0007185175 scopus 로고    scopus 로고
    • LO, A. Y. (1982). Bayesian nonparametric statistical inference for Poisson point processes. Z. Wahrsch. Verw. Gebiete 59 55-66. MR643788
    • LO, A. Y. (1982). Bayesian nonparametric statistical inference for Poisson point processes. Z. Wahrsch. Verw. Gebiete 59 55-66. MR643788
  • 32
    • 0000396415 scopus 로고
    • On a class of Bayesian nonparametric estimates. II. Hazard rate estimates
    • MR1006487
    • LO, A. Y. and WENG, C.-S. (1989). On a class of Bayesian nonparametric estimates. II. Hazard rate estimates. Ann. Inst. Statist. Math. 41 227-245. MR1006487
    • (1989) Ann. Inst. Statist. Math , vol.41 , pp. 227-245
    • LO, A.Y.1    WENG, C.-S.2
  • 33
    • 12344337317 scopus 로고    scopus 로고
    • Bayesian nonparametric survival analysis via Lévy driven Markov processes
    • MR2126344
    • NIETO-BARAJAS, L. E. and WALKER, S. G. (2004). Bayesian nonparametric survival analysis via Lévy driven Markov processes. Statist. Sinica 14 1127-1146. MR2126344
    • (2004) Statist. Sinica , vol.14 , pp. 1127-1146
    • NIETO-BARAJAS, L.E.1    WALKER, S.G.2
  • 34
    • 27844436105 scopus 로고    scopus 로고
    • A semi-parametric Bayesian analysis of survival data based on Lévy-driven processes
    • MR2213503
    • NIETO-BARAJAS, L. E. and WALKER, S. G. (2005). A semi-parametric Bayesian analysis of survival data based on Lévy-driven processes. Lifetime Data Anal. 11 529-543. MR2213503
    • (2005) Lifetime Data Anal , vol.11 , pp. 529-543
    • NIETO-BARAJAS, L.E.1    WALKER, S.G.2
  • 35
    • 84869253824 scopus 로고    scopus 로고
    • NUALART, D. and VIVES, J. (1990). Anticipative calculus for the Poisson process based on the Fock space. In Séminaire de Probabilités XXIV, 1988/89. Lecture Notes in Mathematics 1426 154-165. Springer, Berlin. MR1071538
    • NUALART, D. and VIVES, J. (1990). Anticipative calculus for the Poisson process based on the Fock space. In Séminaire de Probabilités XXIV, 1988/89. Lecture Notes in Mathematics 1426 154-165. Springer, Berlin. MR1071538
  • 36
    • 0042338586 scopus 로고    scopus 로고
    • On the convergence of multiple random integrals
    • MR1874695
    • PECCATI, G. (2001). On the convergence of multiple random integrals. Studia Sci. Math. Hungar. 37 429-470. MR1874695
    • (2001) Studia Sci. Math. Hungar , vol.37 , pp. 429-470
    • PECCATI, G.1
  • 38
    • 63049136456 scopus 로고    scopus 로고
    • Central limit theorems for double Poisson integrals
    • To appear
    • PECCATI, G. and TAQQU, M. S. (2007). Central limit theorems for double Poisson integrals. Bernoulli. To appear.
    • (2007) Bernoulli
    • PECCATI, G.1    TAQQU, M.S.2
  • 39
    • 34247158663 scopus 로고    scopus 로고
    • Stable convergence of generalized L2 stochastic integrals and the principle of conditioning
    • electronic, MR2299924
    • PECCATI, G. and TAQQU, M. S. (2007). Stable convergence of generalized L2 stochastic integrals and the principle of conditioning. Electron. J. Probab. 12 no. 15, 447-480 (electronic). MR2299924
    • (2007) Electron. J. Probab , vol.12 , Issue.15 , pp. 447-480
    • PECCATI, G.1    TAQQU, M.S.2
  • 40
    • 85007107687 scopus 로고    scopus 로고
    • PECCATI, G. and TUDOR, C. A. (2005). Gaussian limits for vector-valued multiple stochastic integrals. In Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics 1857 247-262. Springer, Berlin. MR2126978
    • PECCATI, G. and TUDOR, C. A. (2005). Gaussian limits for vector-valued multiple stochastic integrals. In Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics 1857 247-262. Springer, Berlin. MR2126978
  • 41
    • 0036432576 scopus 로고    scopus 로고
    • Theory and numerical analysis for exact distributions of functionals of a Dirichlet process
    • MR1936323
    • REGAZZINI, E., GUGLIELMI, A. and DI NUNNO, G. (2002). Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30 1376-1411. MR1936323
    • (2002) Ann. Statist , vol.30 , pp. 1376-1411
    • REGAZZINI, E.1    GUGLIELMI, A.2    DI NUNNO, G.3
  • 42
    • 0038702581 scopus 로고    scopus 로고
    • Distributional results for means of normalized random measures with independent increments
    • MR1983542
    • REGAZZINI, E., LIJOI, A. and PRÜNSTER, I. (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist. 31 560-585. MR1983542
    • (2003) Ann. Statist , vol.31 , pp. 560-585
    • REGAZZINI, E.1    LIJOI, A.2    PRÜNSTER, I.3
  • 43
    • 0031526259 scopus 로고    scopus 로고
    • Stochastic integrals: A combinatorial approach
    • MR1457619
    • ROTA, G.-C. and WALLSTROM, T. C. (1997). Stochastic integrals: A combinatorial approach. Ann. Probab. 25 1257-1283. MR1457619
    • (1997) Ann. Probab , vol.25 , pp. 1257-1283
    • ROTA, G.-C.1    WALLSTROM, T.C.2
  • 44
    • 84869244521 scopus 로고    scopus 로고
    • SATO, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics 68. Cambridge Univ. Press, Cambridge. (Translated from the Japanese.) MR1739520
    • SATO, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics 68. Cambridge Univ. Press, Cambridge. (Translated from the Japanese.) MR1739520
  • 45
    • 63049118095 scopus 로고    scopus 로고
    • SURGAILIS, D. (1984). On multiple Poisson stochastic integrals and associated Markov semigroups. Probab. Math. Statist. 3 217-239. MR7641.48
    • SURGAILIS, D. (1984). On multiple Poisson stochastic integrals and associated Markov semigroups. Probab. Math. Statist. 3 217-239. MR7641.48
  • 46
    • 84869257465 scopus 로고    scopus 로고
    • SURGAILIS, D. (2003). Non-CLTs: U-statistics, multinomial formula and approximations of multiple Itô-Wiener integrals. In Theory and Applications of Long-Range Dependence (P. Doukhan, G. Oppenheim and M.S. Taqqu, eds.) 129-142. Birkhäuser, Boston, MA. MR1956047
    • SURGAILIS, D. (2003). Non-CLTs: U-statistics, multinomial formula and approximations of multiple Itô-Wiener integrals. In Theory and Applications of Long-Range Dependence (P. Doukhan, G. Oppenheim and M.S. Taqqu, eds.) 129-142. Birkhäuser, Boston, MA. MR1956047
  • 47
    • 0032339701 scopus 로고    scopus 로고
    • A full Bayesian non-parametric analysis involving a neutral to the right process
    • MR1666808
    • WALKER, S. and DAMIEN, P. (1998). A full Bayesian non-parametric analysis involving a neutral to the right process. Scand. J. Statist. 25 669-680. MR1666808
    • (1998) Scand. J. Statist , vol.25 , pp. 669-680
    • WALKER, S.1    DAMIEN, P.2
  • 48
    • 0031508902 scopus 로고    scopus 로고
    • WALKER, S. and MULIERE, P. (1997). Beta-Stacy processes and a generalization of the Pólyaurn scheme. Ann. Statist. 25 1762-1780. MR1463574
    • WALKER, S. and MULIERE, P. (1997). Beta-Stacy processes and a generalization of the Pólyaurn scheme. Ann. Statist. 25 1762-1780. MR1463574
  • 49
    • 0001121317 scopus 로고    scopus 로고
    • Poisson/gamma random field models for spatial statistics
    • MR1649114
    • WOLPERT, R. L. and ICKSTADT, K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika 85 251-267. MR1649114
    • (1998) Biometrika , vol.85 , pp. 251-267
    • WOLPERT, R.L.1    ICKSTADT, K.2
  • 50
    • 19844375289 scopus 로고    scopus 로고
    • Fractional Ornstein-Uhlenbeck Levy processes and the Telecom process
    • WOLPERT, R. L. and TAQQU, R. L. (2005). Fractional Ornstein-Uhlenbeck Levy processes and the Telecom process. Signal Process. 85 1523-1545.
    • (2005) Signal Process , vol.85 , pp. 1523-1545
    • WOLPERT, R.L.1    TAQQU, R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.