Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value at risk. The variance of the weighted sample quantile estimator is usually a difficult quantity to compute. In this paper we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles ofweighted empirical distributions. Under regular...

Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and maximize the likelihood function. While importance sampling methods have allowed for the accurate evaluation of likelihoods at fixed parameter values, there...

Research has found that value–behavior relations are usually weak to moderate. But is this really the case? This paper proposes of personal values behavior stronger at higher levels value importance and weaker lower levels. In a large, heterogeneous sample, we tested proposition by estimating quantile correlations between self-reported everyday behavior, different locations along distribution i...

Let (Xn : n ≥ 0) be a sequence of iid rv’s with mean zero and finite variance. We present an efficient statedependent importance sampling algorithm for estimating the tail of Sn = X1 + ...+Xn in a large deviations framework as n ↗ ∞. Our algorithm can be shown to be strongly efficient basically throughout the whole large deviations region as n ↗ ∞ (in particular, for probabilities of the form P...

This paper presents a method for estimating the probability μ of a union of J rare events. The method uses n samples, each of which picks one of the rare events at random, samples conditionally on that rare event happening and counts the total number of rare events that happen. We call it ALORE, for ‘at least one rare event’. The ALORE estimate is unbiased and has a coefficient of variation no ...

In this paper we study the rare event of overflow in a Markov fluid queue with finite buffer and many input sources. The probability of this rare event will be estimated by simulations. We present a highly efficient importance sampling procedure to speed up the simulations. The implemented change of meausure is suggested after a large deviations analysis of the overflow probability. This analys...

Some researchers based on the distinction theory, believe that religious influence on other spheres of social life reduce and in spite of traditional life spheres lead by a set of its values, not by a coherent unit and driven by fragmentation theory of values.  The effect of religion on public life and private areas such as work and family over the area of public policy is effective. The relat...

In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer’s theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance sampling are used in rare event simulation for option pricing. We finally focu...

In this paper a new generation of particle filters for nonlinear discrete time processes is proposed, based on convolution kernel probability density estimation. The main advantage of this approach is to be free of the limitations encountered by the current particle filters when the likelihood of the observation variable is analytically unknown or when the observation noise is null or too small...