Journal ArticleDOI
One-step saddlepoint approximations for quantiles
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TLDR
In this paper, two simple one-step methods for approximating distribution quantiles of statistics are derived by approximately inverting saddlepoint formulas for the cumulative distribution functions of the sample mean, which are suitable for use with a pocket calculator.About:
This article is published in Computational Statistics & Data Analysis.The article was published on 1995-07-01. It has received 14 citations till now. The article focuses on the topics: Quantile & Conditional probability distribution.read more
Citations
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Tree-structured wavelet estimation in a mixed effects model for Spectra of replicated time series
TL;DR: In this article, a method for estimating the spectrum of a stationary process using time series traces recorded from experimental designs is proposed, which combines spatially adaptive smoothing methods with recursive dyadic partitioning to construct a model for predicting subject specific effects.
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Symbolic computation for approximating distributions of some families of one and two-sample nonparametric test statistics
TL;DR: The effectiveness of symbolic computation is illustrated to evaluate the saddlepoint approximation for the likelihood ratio, the exponential score, and the Wald-Wolfowitz test statistics.
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A saddlepoint approximation for testing exponentiality against some increasing failure rate alternatives
TL;DR: In this paper, the authors discuss uniformly most powerful unbiased tests for testing exponentiality against a specific class of two-parameter exponential models with increasing failure rate, and show that the optimal test statistic for this problem admits an alternative representation in terms of a spacings statistic.
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Value at Ruin and Tail Value at Ruin of the Compound Poisson Process with Diffusion and Efficient Computational Methods
TL;DR: In this article, the authors consider the capital required to have fixed probability of ruin as a measure of risk and then a coherent extension of it, analogous to the tail value at risk, and show how both measures of risk can be efficiently computed by the saddlepoint approximation.
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Saddlepoint approximations to the distribution of the total distance of the multivariate isotropic and von Mises–Fisher random walks
TL;DR: In this article, saddlepoint approximations to the density and upper tail probabilities of the total distance covered by the random walk are derived, i.e., of the length of the resultant, for a random walk over Rp, where the directions taken by individual steps follow either the isotropic or the vonMises-Fisher distribution.
References
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Journal ArticleDOI
Saddlepoint Approximations in Statistics
TL;DR: In this paper, it was shown that for a statistic such as the mean of a sample of size $n, or the ratio of two such means, a satisfactory approximation to its probability density, when it exists, can be obtained nearly always by the method of steepest descents.
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Saddle point approximation for the distribution of the sum of independent random variables
Robert Lugannani,Stephen O Rice +1 more
TL;DR: In this article, a uniform asymptotic series for the probability distribution of the sum of a large number of independent random variables is derived, which is based on the fact that the major components of the distribution are determined by a saddle point and a singularity.
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Tail Probability Approximations
TL;DR: In this article, two explicit approximation formulae for the tail probability of a sample mean are discussed, one based on the classical Edgeworth expansion of the exponentially shifted density recentred at the mean and the other based on an apparently unrelated formula due to Lugannani & Rice (1980) which controls the relative error uniformly over the whole range of the mean.
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Saddlepoint Methods and Statistical Inference
TL;DR: In this article, the authors present a survey of second order asymptotic inference using the saddlepoint method, including Barndorff-Nielsen's approximation to the distribution of the maximum likelihood estimate, Bartlett factors for the likelihood ratio statistic and approximations to predictive and conditional likelihood.