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Saddlepoint approximations

, 2015
The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is
Gatto, Riccardo, Riccardo Gatto
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Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance

Applied Mathematical Finance, 2014
We consider the saddlepoint approximation methods for pricing derivatives whose payoffs depend on the discrete realized variance of the underlying price process of a risky asset.
Wendong Zheng, Yue Kuen Kwok
exaly   +2 more sources

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On the bootstrap saddlepoint approximations

Biometrika, 1994
Summary: 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, Feuerverger, Andrey, Robinson, John   +2 more
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An improved saddlepoint approximation

Mathematical Biosciences, 2007
Given 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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Likelihood Estimation for the INAR(p) Model by Saddlepoint Approximation

Journal of the American Statistical Association, 2015
Saddlepoint techniques have been used successfully in many applications, owing to the high accuracy with which they can approximate intractable densities and tail probabilities.
Xanthi Pedeli, A C Davison, Konstantinos Fokianos   +2 more
exaly   +1 more source

Saddlepoint approximations in resampling methods

Biometrika, 1988
Summary: 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, 1980
SUMMARY 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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Saddlepoint Approximations for Regression Models

Biometrika, 1991
SUMMARY This paper uses the techniques of saddlepoint or tilted-exponential approximation to develop an approximation to the small-sample distribution of estimators defined by a system of estimating equations when observations are independently but not identically distributed. This allows for the explicit treatment of models with explanatory variables.
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Saddlepoint approximations

1995
Abstract Although introduced more than 60 years ago it is only during the last 15 years that there has been a systematic development of saddlepoint approximations. These approximations give a highly accurate expression for the tail of a distribution, not only in the centre of the distribution but also for very small tail probabilities.
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Saddlepoint approximations for estimating equations

Biometrika, 1983
Let X be a random variable (or a random vector) with probability density f(x,\(\theta)\). The function \(\Psi (x,\theta)\) is assumed to be monotonically decreasing in \(\theta\) for all x and \(E\Psi(X,\theta)=0\) for all \(\theta\). Given a random sample \(x_ 1,...,x_ n\) from such a distribution, an estimate of \(\theta\) is provided by the unique ...
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