Saddlepoint Approximations in Statistics

Daniels, H. E.

doi:10.1214/aoms/1177728652

Cited by 986 publications

(587 citation statements)

References 9 publications

Supporting

Mentioning

571

Contrasting

Unclassified

Order By: Relevance

“…Daniels [22] introduced the saddlepoint method to statistics in order to approximate the probability density function (PDF) of the mean of i.i.d. random variables X i 's.…”

Section: Saddlepoint Approximationmentioning

confidence: 99%

“…Daniels [22] used the method of steepest descent to expand this contour integral. The saddlepointẑ is defined by the saddlepoint equation K (ẑ) = x; the modulus of the integrand is minimized along the real axis atẑ and maximized atẑ along the contour parallel to the imaginary axis passing throughẑ.…”

Section: Saddlepoint Approximationmentioning

confidence: 99%

“…The saddlepoint method is rooted in asymptotic expansions for evaluating contour integrals in the complex plane. It was introduced in statistics by Daniels [22] to approximate the probability density function of the sum of independent random variables. Lugannani and Rice [42] derive a saddlepoint approximation for the distribution function.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Saddlepoint approximations for affine jump-diffusion models

Glasserman¹,

Kim²

2009

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

“…Daniels [22] introduced the saddlepoint method to statistics in order to approximate the probability density function (PDF) of the mean of i.i.d. random variables X i 's.…”

Section: Saddlepoint Approximationmentioning

confidence: 99%

Section: Saddlepoint Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Saddlepoint approximations for affine jump-diffusion models

Glasserman¹,

Kim²

2009

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

“…The test statistic is given by an explicit formula, is nonparametric, and it does not require the estimation of the sparsity function. It is derived from the results in Robinson, Ronchetti, & Young (2003) for M −estimators, which were obtained using saddlepoint techniques (Daniels (1954)) and can be viewed as an empirical likelihood procedure based on tilted exponential weights; cf. the discussion in Ma & Ronchetti (2011), p. 148.…”

Section: Introductionmentioning

confidence: 99%

Saddlepoint tests for quantile regression

Ronchetti

Sabolová

2016

Can J Statistics

View full text Add to dashboard Cite

Quantile regression is a flexible and powerful technique which allows to model the quantiles of the conditional distribution of a response variable given a set of covariates. Regression quantile estimators can be viewed as M −estimators and standard asymptotic inference is readily available based on likelihoodratio, Wald, and score-type test statistics. However, these statistics require the estimation of the sparsity function s(α) = [g(G −1 (α))] −1 , where G and g are the cumulative distribution function and the density of the regression errors respectively, and this can lead to nonparametric density estimation. Moreover, the asymptotic χ 2 distribution for these statistics can provide an inaccurate approximation of tail probabilities and this can lead to inaccurate p-values, especially for moderate sample sizes. Alternative methods which do not require the estimation of the sparsity function, include rank techniques and resampling methods to obtain confidence intervals, which can be inverted to test hypotheses. These are typically more accurate than the standard M − tests.In this paper we show how accurate tests can be obtained by using a nonparametric saddlepoint test statistic. The proposed statistic is asymptotically χ 2 distributed, does not require the specification of the error distribution, and does not require the estimation of the sparsity function. The validity of the method is demonstrated through a simulation study, which shows both the robustness and the accuracy of the new test compared to the best available alternatives.The Canadian Journal of , où G et g sont la fonction de répartition et la fonction de densité des erreurs respectivement et ceci demande de l'estimation nonparamétrique. En plus la distribution asymptotique χ 2 de ces statistiques peut donner lieuà des approximations peu précises des probabilités dans les queues de la distribution et ceci peut produire des p−valeurs imprécises surtout dans le cas d'échantillons de taille moyenne. Des méthodes alternatives qui ne nécessitent pas de l'estimation de la fonction de "sparsity" sont disponibles, par exemple les méthodes de rang et celles de reéchantillonage pour obtenir des intervalles de confiance qui peuventêtre inversés afin de construire des tests. Ces méthodes sont typiquement plus précises que les M −tests standard.Dans cet article on présente une statistique nonparamétrique de pointe de selle qui permet de construire des tests très précis. Elle est asymptotiquement distribuée selon une loi du χ 2 et elle ne nécessite ni de la spécification de la distribution des erreurs ni de l'estimation de la fonction de "sparsity". La performance de la méthode est démontrée par uneétude de simulation, qui montre la robustesse et la précision du nouveau test en comparaison avec les meilleures alternatives disponibles dans la littérature.La revue canadienne de statistique xx: 1-29;

show abstract

“…The saddlepoint approximation is another large deviations approximation which allows to approximate with high accuracy small probabilities of rare events. The saddlepoint approximation in this context originates from Daniels (1954) and Lugannani and Rice (1980). Gatto and Mosimann (2012) and Gatto and Baumgartner (2014) provide comparisons between importance sampling and the saddlepoint approximation, for probabilities of ruin in finite and infinite time horizons, however only for the compound Poisson process with Wiener perturbation.…”

Section: Introductionmentioning

confidence: 99%

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

Gatto

2014

Applied Mathematics and Computation

View full text Add to dashboard Cite

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t, x → ∞, where t > 0 is the time horizon and x > 0 is the starting point of the risk process, with y = t/x held constant and assumed either below or above a certain constant. Key words and phrasesBounded relative error; exponential tilt; Legendre-Fenchel transform; logarithmic efficiency; Lundberg conjugated measure; ruin due to creeping and to jump; ruin past a finite time horizon, within a finite and the infinite time horizons; saddlepoint approximation; short and long time horizons.

show abstract

Saddlepoint Approximations in Statistics

Cited by 986 publications

References 9 publications

Saddlepoint approximations for affine jump-diffusion models

Saddlepoint approximations for affine jump-diffusion models

Saddlepoint tests for quantile regression

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

Contact Info

Product

Resources

About