×

Higher-order approximations to conditional distribution functions. (English) Zbl 0897.62016

Summary: This paper derives higher-order terms in the double-saddlepoint expansion of I. M. Skovgaard [J. Appl. Probab. 24, No. 4, 875-887 (1987; Zbl 0638.62018)] for a unidimensional conditional cumulative distribution function. Expansions for continuous and lattice random variables are derived. Results are applied to the sufficient statistic in logistic regression.

MSC:

62E17 Approximations to statistical distributions (nonasymptotic)
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0638.62018
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] BEDRICK, E. J. and HILL, J. R. 1992. An empirical assessment of saddlepoint approximations for testing a logistic regression parameter. Biometrics 48 529 544. Z.
[2] BOCHNER, S. and MARTIN, W. T. 1948. Several Complex Variables. Princeton Univ. Press. Z. · Zbl 0041.05205
[3] COX, D. R. and SNELL, E. J. 1989. Analy sis of Binary Data. Chapman and Hall, London. Z.
[4] DAVISON, A. C. 1988. Approximate conditional inference in generalized linear models. J. Roy. Statist. Soc. Ser. B 50 445 461. Z. JSTOR:
[5] GORDON, T. and FOSS, B. M. 1966. The role of stimulation in the delay of onset of crying in the new-born infant. Journal of Experimental Psy chology 16 79 81. Z.
[6] HOCKING, R. R. 1985. The Analy sis of Linear Models. Brooks Cole, Monterey, CA. Z.
[7] JENSEN, J. L. 1991. Uniform saddlepoint approximations and log-concave densities. J. Roy. Statist. Soc. Ser. B 53 157 172. JSTOR: · Zbl 0800.62081
[8] KOLASSA, J. E. 1994. Series Approximation Methods in Statistics. Springer, New York. Z. · Zbl 0797.62008
[9] KOLASSA, J. E. and MCCULLAGH, P. 1990. Edgeworth series for lattice distributions. Ann. Statist. 18 981 985. Z. · Zbl 0703.62021 · doi:10.1214/aos/1176347637
[10] KOLASSA, J. E. and TANNER, M. A. 1994. Approximate conditional inference in exponential families via the Gibbs sampler. J. Amer. Statist. Assoc. 89 697 702. Z. JSTOR: · Zbl 0803.62013 · doi:10.2307/2290874
[11] MCCULLAGH, P. 1987. Tensor Methods in Statistics. Chapman and Hall, London. Z. · Zbl 0732.62003
[12] MEHTA, C. R., PATEL, N. R. and SENCHAUDHURI, P. 1993. Smart Monte Carlo methods for conditional logistic regression. Unpublished manuscript. Z.
[13] SKOVGAARD, I. M. 1987. Saddlepoint expansions for conditional distributions. J. Appl. Probab. 24 875 887. Z. JSTOR: · Zbl 0638.62018 · doi:10.2307/3214212
[14] TEMME, N. M. 1982. The uniform asy mptotic expansion of a class of integrals related to cumulative distribution functions. SIAM J. Math. Anal. 13 239 252. · Zbl 0489.41031 · doi:10.1137/0513017
[15] EVANSTON, ILLINOIS 60208
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.