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Volumn 95, Issue 452, 2000, Pages 1358-1364

Higher-Order Asymptotic Approximation: Laplace, Saddlepoint, and Related Methods

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EID: 0442324994     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10474348     Document Type: Article
Times cited : (14)

References (54)
  • 2
    • 0003406635 scopus 로고    scopus 로고
    • 2nd ed.), New York: Springer-Verlag
    • Bak, J., and Newman, D. J. (1996), Complex Analysis (2nd ed.), New York: Springer-Verlag.
    • (1996) Complex Analysis
    • Bak, J.1    Newman, D.J.2
  • 3
    • 0000883264 scopus 로고
    • Conditionality Resolutions
    • Barndorff-Nielsen, O. E. (1980), “Conditionality Resolutions,” Biometrika, 67, 293-310.
    • (1980) Biometrika , vol.67 , pp. 293-310
    • Barndorff-Nielsen, O.E.1
  • 4
    • 0000072546 scopus 로고
    • On a Formula for the Distribution of the Maximum Likelihood Estimator
    • Barndorff-Nielsen, O. E. (1983), “On a Formula for the Distribution of the Maximum Likelihood Estimator,” Biometrika, 70, 343-365.
    • (1983) Biometrika , vol.70 , pp. 343-365
    • Barndorff-Nielsen, O.E.1
  • 5
    • 0001667622 scopus 로고
    • Inference on Full and Partial Parameters Based on Standardized Signed Log-Likelihood Ratio
    • Barndorff-Nielsen, O. E. (1986), “Inference on Full and Partial Parameters Based on Standardized Signed Log-Likelihood Ratio,” Biometrika, 73, 307-322.
    • (1986) Biometrika , vol.73 , pp. 307-322
    • Barndorff-Nielsen, O.E.1
  • 6
    • 33744704361 scopus 로고
    • Discussion of “Saddlepoint Methods and Statistical Inference,” by N. Reid
    • Barndorff-Nielsen, O. E. (1988), Discussion of “Saddlepoint Methods and Statistical Inference,” by N. Reid, Statistical Science, 3, 288-289.
    • (1988) Statistical Science , vol.3 , pp. 288-289
    • Barndorff-Nielsen, O.E.1
  • 8
    • 0000596503 scopus 로고
    • Modified Signed Log-Likelihood Ratio
    • Barndorff-Nielsen, O. E. (1991), “Modified Signed Log-Likelihood Ratio,” Biometrika, 78, 557-563.
    • (1991) Biometrika , vol.78 , pp. 557-563
    • Barndorff-Nielsen, O.E.1
  • 9
    • 0000342633 scopus 로고
    • Adjusted Versions of Profile Likelihood and Directed Likelihood, and Extended Likelihood
    • Barndorff-Nielsen, O. E. (1994), “Adjusted Versions of Profile Likelihood and Directed Likelihood, and Extended Likelihood,” Journal of the Royal Statistical Society, Ser. B, 56, 125-140.
    • (1994) Journal of the Royal Statistical Society, Ser. B , vol.56 , pp. 125-140
    • Barndorff-Nielsen, O.E.1
  • 13
    • 0012999843 scopus 로고
    • On the Validity of Edgeworth and Saddlepoint Approximations
    • Booth, J., Hall, P., and Wood, A. T. A. (1994), “On the Validity of Edgeworth and Saddlepoint Approximations,” Journal of Multivariate Analysis, 51, 121-138.
    • (1994) Journal of Multivariate Analysis , vol.51 , pp. 121-138
    • Booth, J.1    Hall, P.2    Wood, A.T.A.3
  • 14
    • 33744687039 scopus 로고
    • Discussion of “The Roles of Conditioning in Inference,” by N. Reid
    • Casella, G., DiCiccio, T. J., and Wells, M. T. (1995), Discussion of “The Roles of Conditioning in Inference,” by N. Reid, Statistical Science, 10, 138-199.
    • (1995) Statistical Science , vol.10 , pp. 138-199
    • Casella, G.1    Diciccio, T.J.2    Wells, M.T.3
  • 15
    • 0001367156 scopus 로고
    • Saddlepoint Approximations in Statistics
    • Daniels, H. (1954), “Saddlepoint Approximations in Statistics,” Annals of Mathematical Statistics, 25, 631-650.
    • (1954) Annals of Mathematical Statistics , vol.25 , pp. 631-650
    • Daniels, H.1
  • 16
    • 0011284410 scopus 로고
    • Discussion of “The Regression Analysis of Binary Se-quences” by D. R. Cox
    • Daniels, H. (1958), Discussion of “The Regression Analysis of Binary Se-quences” by D. R. Cox, Journal of the Royal Statistical Society, Ser. B, 20, 236-238.
    • (1958) Journal of the Royal Statistical Society, Ser. B , vol.20 , pp. 236-238
    • Daniels, H.1
  • 17
    • 0002600304 scopus 로고
    • Saddlepoint Approximations for Estimating Equations
    • Daniels, H. (1983), “Saddlepoint Approximations for Estimating Equations,” Biometrika, 70, 89-96.
    • (1983) Biometrika , vol.70 , pp. 89-96
    • Daniels, H.1
  • 18
  • 20
    • 0000100727 scopus 로고
    • Approximate Conditional Inference in Generalized Linear Models
    • Davison, A. C. (1988), “Approximate Conditional Inference in Generalized Linear Models,” Journal of the Royal Statistical Society, Ser. B, 50,445-461.
    • (1988) Journal of the Royal Statistical Society, Ser. B , vol.50 , pp. 445-461
    • Davison, A.C.1
  • 22
    • 0040758907 scopus 로고
    • Näherungsformeln für die Zylinderfunktionen für Grosse Werte des Arguments und Unbeschränkt Veränderliche Werte des Index
    • Debye, P. (1909), “Näherungsformeln für die Zylinderfunktionen für Grosse Werte des Arguments und Unbeschränkt Veränderliche Werte des Index,” Math. Ann., 67, 535-558.
    • (1909) Math. Ann. , vol.67 , pp. 535-558
    • Debye, P.1
  • 24
    • 0011024305 scopus 로고
    • Approximations of Marginal Tail Probabilities for a Class of Smooth Functions With Applications to Bayesian and Conditional Inference
    • DiCiccio, T. J., and Martin, M. A. (1991), “Approximations of Marginal Tail Probabilities for a Class of Smooth Functions With Applications to Bayesian and Conditional Inference,” Biometrika, 78, 891-902.
    • (1991) Biometrika , vol.78 , pp. 891-902
    • Diciccio, T.J.1    Martin, M.A.2
  • 25
    • 0342996538 scopus 로고
    • Analytical Approximations to Conditional Distribution Functions
    • DiCiccio, T. J., and Martin, M. A. (1993), “Analytical Approximations to Conditional Distribution Functions,” Biometrika, 80, 781-790.
    • (1993) Biometrika , vol.80 , pp. 781-790
    • Diciccio, T.J.1    Martin, M.A.2
  • 26
    • 0001609615 scopus 로고
    • Normed Likelihood as Saddlepoint Approximation
    • Fraser, D. A. S. (1988), “Normed Likelihood as Saddlepoint Approximation,” Journal of Multivariate Analysis, 27, 181-193.
    • (1988) Journal of Multivariate Analysis , vol.27 , pp. 181-193
    • Fraser, D.A.S.1
  • 27
    • 78751701119 scopus 로고
    • Tail Probabilities From Observed Likelihoods
    • Fraser, D. A. S. (1990), “Tail Probabilities From Observed Likelihoods,” Biometrika, 77, 65-76.
    • (1990) Biometrika , vol.77 , pp. 65-76
    • Fraser, D.A.S.1
  • 28
    • 85011132547 scopus 로고
    • Asymptotics I: A Note on Laplaces Method,”
    • Fulks, W. (1960), “Asymptotics I: A Note on Laplace’s Method,” American Mathematical Monthly, 67, 880-882.
    • (1960) American Mathematical Monthly , vol.67 , pp. 880-882
    • Fulks, W.1
  • 29
    • 84972540015 scopus 로고
    • Asymptotics II: Laplaces Method for Multiple Integrals,”
    • Fulks, W., and Sather, J. O. (1961), “Asymptotics II: Laplace’s Method for Multiple Integrals,” Pacific Journal of Mathematics, 11, 185-192.
    • (1961) Pacific Journal of Mathematics , vol.11 , pp. 185-192
    • Fulks, W.1    Sather, J.O.2
  • 30
    • 0000736067 scopus 로고    scopus 로고
    • Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling
    • Gelman, A., and Meng, X-L. (1998), “Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling” (with discussion), Statistical Science, 13, 163-185.
    • (1998) Statistical Science , vol.13 , pp. 163-185
    • Gelman, A.1    Meng, X.-L.2
  • 31
    • 0040061088 scopus 로고    scopus 로고
    • Stochastic Integration Rules for Infinite Regions
    • Genz, A., and Monahan, J. (1998), “Stochastic Integration Rules for Infinite Regions,” SIAM Journal on Scientific Computing, 19, 426-439.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , pp. 426-439
    • Genz, A.1    Monahan, J.2
  • 33
    • 0012983316 scopus 로고
    • Asymptotics in Bayesian Computation
    • J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Oxford, U.K.: Clarendon Press
    • Kass, R. E., Tierney, L., and Kadane, J. B. (1988), “Asymptotics in Bayesian Computation,” in Bayesian Statistics 3, eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Oxford, U.K.: Clarendon Press.
    • (1988) Bayesian Statistics , vol.3
    • Kass, R.E.1    Tierney, L.2    Kadane, J.B.3
  • 34
    • 0033243861 scopus 로고    scopus 로고
    • Convergence and Accuracy of Gibbs Sampling for Conditional Distributions in Generalized Linear Models
    • Kolassa, J. (1999), “Convergence and Accuracy of Gibbs Sampling for Conditional Distributions in Generalized Linear Models,” The Annals of Statistics, 27, 129-142.
    • (1999) The Annals of Statistics , vol.27 , pp. 129-142
    • Kolassa, J.1
  • 35
    • 21344487659 scopus 로고
    • Approximate Conditional Inference in Exponential Families via the Gibbs Sampler
    • Kolassa, J., and Tanner, M. A. (1994), “Approximate Conditional Inference in Exponential Families via the Gibbs Sampler,” Journal of the American Statistical Association, 89, 697-702.
    • (1994) Journal of the American Statistical Association , vol.89 , pp. 697-702
    • Kolassa, J.1    Tanner, M.A.2
  • 36
    • 0001303107 scopus 로고
    • A Note on Gauss-Hermite Quadrature
    • Liu, Q., and Pierce, D. (1994), “A Note on Gauss-Hermite Quadrature,” Biometrika, 81, 624-629.
    • (1994) Biometrika , vol.81 , pp. 624-629
    • Liu, Q.1    Pierce, D.2
  • 37
    • 0000660352 scopus 로고
    • Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables
    • Lugannani, R., and Rice, S. O. (1980), “Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables,” Advances in Applied Probability, 12, 475-590.
    • (1980) Advances in Applied Probability , vol.12 , pp. 475-590
    • Lugannani, R.1    Rice, S.O.2
  • 39
    • 0001482702 scopus 로고
    • Practical Use of Higher-Order Asymptotics for Multiparameter Exponential Families
    • Pierce, D., and Peters, D. (1992), “Practical Use of Higher-Order Asymptotics for Multiparameter Exponential Families” (with discussion), Journal of the Royal Statistical Society, Ser. B, 54, 701-725.
    • (1992) Journal of the Royal Statistical Society, Ser. B , vol.54 , pp. 701-725
    • Pierce, D.1    Peters, D.2
  • 40
    • 84972517956 scopus 로고
    • “The Roles of Conditioning in Inference
    • Reid, N. (1995), “The Roles of Conditioning in Inference” (with discussion), Statistical Science, 10, 138-157.
    • (1995) Statistical Science , vol.10 , pp. 138-157
    • Reid, N.1
  • 41
    • 0030304445 scopus 로고    scopus 로고
    • Likelihood and Higher-Order Approximations to Tail Areas: A Review and Annotated Bibliography
    • Reid, N. (1996), “Likelihood and Higher-Order Approximations to Tail Areas: A Review and Annotated Bibliography,” Canadian Journal of Statistics, 24, 263-278.
    • (1996) Canadian Journal of Statistics , vol.24 , pp. 263-278
    • Reid, N.1
  • 44
    • 0003006735 scopus 로고
    • Saddlepoint Approximations for Permutation Tests and Confidence Intervals
    • Robinson, J. (1982), “Saddlepoint Approximations for Permutation Tests and Confidence Intervals,” Journal of the Royal Statistical Society, Ser. B, 44, 91-101.
    • (1982) Journal of the Royal Statistical Society, Ser. B , vol.44 , pp. 91-101
    • Robinson, J.1
  • 45
    • 0007223315 scopus 로고    scopus 로고
    • An Empirical Adjustment to the Likelihood Ratio Statistic
    • Severini, T. (1999), “An Empirical Adjustment to the Likelihood Ratio Statistic,” Biometrika, 86, 235-248.
    • (1999) Biometrika , vol.86 , pp. 235-248
    • Severini, T.1
  • 46
    • 0011317516 scopus 로고
    • On Secant Approximations to Cumulative Distribution Functions
    • Skates, S. (1993), “On Secant Approximations to Cumulative Distribution Functions,” Biometrika, 80, 223-235.
    • (1993) Biometrika , vol.80 , pp. 223-235
    • Skates, S.1
  • 47
    • 0000045884 scopus 로고
    • Saddlepoint Expansions for Conditional Distributions
    • Skovgaard, I. (1987), “Saddlepoint Expansions for Conditional Distributions,” Journal of Applied Probability, 24, 875-887.
    • (1987) Journal of Applied Probability , vol.24 , pp. 875-887
    • Skovgaard, I.1
  • 49
    • 0042416886 scopus 로고    scopus 로고
    • Approximately Exact Inference for the Common Odds Ratio in Several 2x2 Tables
    • Strawderman, R. L., and Wells, M. T. (1998), “Approximately Exact Inference for the Common Odds Ratio in Several 2x2 Tables” (with discussion), Journal of the American Statistical Association, 93, 1294-1306.
    • (1998) Journal of the American Statistical Association , vol.93 , pp. 1294-1306
    • Strawderman, R.L.1    Wells, M.T.2
  • 50
    • 84950871099 scopus 로고
    • Accurate Approximations for Posterior Moments and Marginal Densities
    • Tierney, L., and Kadane, J. B. (1986), “Accurate Approximations for Posterior Moments and Marginal Densities,” Journal of the American Statistical Association, 81, 1032-1038.
    • (1986) Journal of the American Statistical Association , vol.81 , pp. 1032-1038
    • Tierney, L.1    Kadane, J.B.2
  • 51
    • 0001560641 scopus 로고
    • Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions
    • Tierney, L., Kass, R. E., and Kadane, J. B. (1989), “Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions,” Journal of the American Statistical Association, 84, 710-716.
    • (1989) Journal of the American Statistical Association , vol.84 , pp. 710-716
    • Tierney, L.1    Kass, R.E.2    Kadane, J.B.3
  • 53
    • 21144473030 scopus 로고
    • Saddlepoint Approximations to the CDF of Some Statistics With Nonnormal Limit Distributions
    • Wood, A. T. A., Booth, J., and Butler, R. (1993), “Saddlepoint Approximations to the CDF of Some Statistics With Nonnormal Limit Distributions,” Journal of the American Statistical Association, 88, 680-686.
    • (1993) Journal of the American Statistical Association , vol.88 , pp. 680-686
    • Wood, A.T.A.1    Booth, J.2    Butler, R.3
  • 54
    • 22444454884 scopus 로고    scopus 로고
    • Better Saddlepoint Confidence Intervals via Bootstrap Calibration
    • Zheng, X. (1998), “Better Saddlepoint Confidence Intervals via Bootstrap Calibration,” Proceedings of the American Mathematical Society, 126, 3669-3679.
    • (1998) Proceedings of the American Mathematical Society , vol.126 , pp. 3669-3679
    • Zheng, X.1


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