Use Of Saddlepoint Approximations Research Articles

On the Use of Saddlepoint Approximations in High Dimensional Inference

Inference in high dimensional parameter space poses many challenges. One of these is the possible use of saddlepoint approximations. Motivated by a recent use of the saddlepoint approximation to construct a conditional test, we argue that the precision is questionable. We illustrate this by an example giving a 50% relative error in the calculation of the p-value. A power study of the underlying test reveals a low power in many situations. As an alternative it is suggested to use the likelihood ratio test.

Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy of the proposed SPA approach.

A Practical Procedure to Find Matching Priors for Frequentist Inference

We present a practical way to find matching priors via the use of saddlepoint approximations and obtain p-values of tests of an interest parameter in the presence of nuisance parameters. The advantages of our procedure are the flexibility in choosing different initial conditions so that one may adjust the performance of a test, and the less intensive computational efforts compared to a Markov Chain Monto Carlo method.

Saddlepoint approximations for affine jump-diffusion models

Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuous-time asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Duffie et al. [2000. Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343–1376]. Calculating model prices requires inversion of these transforms, and this has limited the application of AJD models to the comparatively small subclass for which the transforms are available in closed form. This article seeks to widen the scope of AJD models amenable to practical application through approximate transform inversion techniques. More specifically, we develop the use of saddlepoint approximations for AJD models. These approximations facilitate the calculation of prices in AJD models whose transforms are not available explicitly. We derive and test several alternative saddlepoint approximations and find that they produce accurate prices over a wide range of parameters.

Boundary Crossing Probabilities for Scan Statistics and Their Applications to Change-Point Detection

This paper gives a brief review of recent developments in change-point detection and in the associated boundary crossing problems. Making use of saddlepoint approximations for Markov random walks, we give further extensions of a basic result on boundary crossing probabilities, leading to detection procedures that are not too de-manding in computational and memory requirements and yet are nearly optimal under several performance criteria.

Saddlepoint approximations to option prices

The use of saddlepoint approximations in statistics is a well-established technique for computing the distribution of a random variable whose moment generating function is known. In this paper, we apply the methodology to computing the prices of various European-style options, whose returns processes are not the Brownian motion with drift assumed in the Black{Scholes paradigm. Through a number of examples, we show that the methodology is generally accurate and fast.

SPIN AND CHARGE FLUCTUATION IN CUPRATE OXIDE SUPERCONDUCTORS

Spin and charge fluctuation are obtained from a two-band model making use of saddle point approximation in path-integral form.

Saddle point bit error rate computations for optical communication systems incorporating equalizers

Bit error rate computations for optical communication systems incorporating equalizers and under both noise and intersymbol interference (ISI) are discussed. An accurate method based on saddle point approximation is used. Previous work using saddle point approximation considered only basic integration-and-dump detection. The use of equalizers other than integration-and-dump complicates the computation because of the complexity of the moment generating function involved. When ISI is strong, use of an equalizer such as raised-cosine filtering is important for ISI reduction. To help optical receiver design, this paper explains the use of saddle point approximation when an equalizer is used. In addition to integration-and-dump, cosine and raised-cosine equalizers are considered for ISI reduction. To study the interdependence between the received waveform and equalizer used, two different input pulses are also considered. To verify the computation accuracy, exact contour integration based on the numerical quadrature method is performed. Results show that saddle point approximation can provide a fast and accurate computation. From the bit error rate (BER) performance computed, it is found that the traditional use of matched filtering has a poor performance when either ISI is strong or the APD gain is large, and the use of a proper equalizer can significantly improve the performance. In other words, the best choice of an equalizer design depends on the input waveform, amount of ISI, and the APD gain. >

An Empirical Assessment of Saddlepoint Approximations for Testing a Logistic Regression Parameter

Saddlepoint methods provide quick and easy approximations to significance levels for conditional tests of logistic regression parameters. We evaluate the accuracies of saddlepoint approximations for three well-known conditional tests: Bartlett's test for no three-factor interaction in a 2 x 2 x 2 table, the test for trend in a series of probabilities, and the exact test of no association in stratified 2 x 2 tables with a common odds ratio. General recommendations are suggested regarding the use of saddlepoint approximations for exact conditional significance levels.