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Efficient Variant Set Mixed Model Association Tests for Continuous and Binary Traits in Large-Scale Whole-Genome Sequencing Studies. [PDF]
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Practical Saddlepoint Approximations
American Statistician, 1999Abstract This article illustrates univariate and conditional saddle-point density and distribution function approximations. The emphasis is on the applications and on the calculations needed to compute the approximations. Uses of the approximations include p value computations for some test statistics, approximations of finite mixture distributions ...
Snehalata Huzurbazar
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Saddlepoint approximations for nonlinear statistics
Canadian Journal of Statistics, 1990AbstractIt is well known that saddlepoint expansions lead to accurate approximations to the cumulative distributions and densities of a sample mean and other simple linear statistics. The use of such expansions is explored in a broader situation. The saddlepoint formula for the tail probability of a certain type of nonlinear statistic is derived.
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An improved saddlepoint approximation
Mathematical Biosciences, 2007Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents.
Gillespie CS, Renshaw E
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Saddlepoint approximations in resampling methods
Biometrika, 1988Summary: Saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications. Examples include mean estimation, ratio estimation, two-sample comparisons, and autoregressive estimation.
Davison, Anthony C., Hinkley, David V.
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Exact Saddlepoint Approximations
Biometrika, 1980SUMMARY The renormalized saddlepoint approximation to the probability density of ani estimator' often has a surprisingly low relative error over the whole admissible range of the parameter. In particular it is known to be exact for certain densities. This raises the question of how to characterize the class of such exact cases.
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On the bootstrap saddlepoint approximations
Biometrika, 1994Summary: We compare saddlepoint approximations to the exact distributions of a Studentized mean and to its bootstrap approximation. We show that, on bounded sets, these empirical saddlepoint approximations achieve second order relative errors uniformly. We also consider the relative errors for larger deviations.
Jing, Bingyi +2 more
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