Results 141 to 150 of about 5,999 (179)

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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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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Uniform saddlepoint approximations

Advances in Applied Probability, 1988
The validity of the saddlepoint expansion evaluated at the pointyis considered in the limitytending to ∞. This is done for the expansions of the density and of the tail probability of the meanofni.i.d. random variables and also for the expansion of the tail probability of a compound Poisson sum, whereNis a Poisson random variable.
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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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On the empirical saddlepoint approximation

Biometrika, 1989
Summary: The properties of the saddlepoint approximation are investigated when the required cumulant generating function is obtained empirically. Properties of the empirical moment generating function and empirical cumulant generating function and derivatives of these processes which are needed for this study are derived first, in particular their ...
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Extended Saddlepoint Approximation Methods

2018
In the previous chapter, we assume that the cumulant generating function (cgf) of the underlying random variable X is known in closed form. The saddlepoint equation involves the first order derivative of the cgf and one can solve for the saddlepoint by a root finding algorithm.
Yue Kuen Kwok, Wendong Zheng
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SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS

Econometric Theory, 2011
This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is ...
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Saddlepoint approximation of CreditRisk+

Journal of Banking & Finance, 2002
Abstract CreditRisk+ is an influential and widely implemented model of portfolio credit risk. As a close variant of models long used for insurance risk, it retains the analytical tractability for which the insurance models were designed. Value-at-risk (VaR) can be obtained via a recurrence-rule algorithm, so Monte Carlo simulation can be avoided ...
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Saddlepoint Approximation for Credit Portfolios

2018
We consider a portfolio of loans or bonds, where the loan borrowers or bond issuers may fail to meet the promised cashflows as stated in the loan contracts or bond indentures. These payment defaults lead to credit losses to the holder of the portfolio of these credit instruments or names (loans or bonds).
Yue Kuen Kwok, Wendong Zheng
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Saddlepoint approximations for subordinator processes

Journal of Statistical Computation and Simulation, 2015
ABSTRACTWe develop the saddlepoint approximations in obtaining the transition functions for general subordinator processes. We derive explicit expressions of the first- and second-order approximations. Specifically, we consider some particular classes of subordinators including the Poisson processes, the Gamma processes, the α-stable subordinators, and
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