We consider nonlinear models with an independent variable that is measured with error. The measurement error can be correlated with the true value, i.e. the measurement error is allowed to be nonclassical. We show that we can use a control variate estimator to estimate the parameters of interest. If we are prepared to make an assumption of the joint distribution of the first-stage and measureme...

Knowledge of either analytical or numerical approximations should enable more efficient simulation estimators to be constructed.” This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. We present a new approach for obtaining variance reduction in Markov process simulation that is applicable to a v...

This note is a complement of the paper " Solving BSDE with adaptive control variate " [1]. It deals with the convergence of the approximating operator P, based on a non parametric regression technique called local averaging, and defined in Definition 1.1. Although the computations are quite standard (see [3], [2]), the specificities of the paper are the following • the support of the variables ...

We study biased control variates (BCVs), whose purpose is to improve the efficiency of stochastic simulation experiments. BCVs replace the control-simulation mean with an approximation; the resulting control-variate estimator is biased. This bias may not be a significant issue for finite sample sizes, however, because our estimator minimizes the more general mean-squared-error (mse), i.e., the ...

The aim of this work is to develop a simulation approach to the yield curve evolution in the Heath, Jarrow & Morton (1992) framework. The stochastic quantities considered as affecting the forward rate volatility function are the spot rate and the forward rate. A decomposition of the volatility function into a Hull & White (1990) volatility and a remainder allows us to develop an efficient Contr...

In the simulation-on-demand paradigm, we invest computational effort by running a simulation experiment before a question is asked, and then we quickly provide an answer by making use of the results of the earlier simulation experiment. This can be done by building a metamodel, but standard metamodeling methods used in stochastic simulation have the disadvantage that they require validation. We...

This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain Φ. The scheme is based on the idea of weak approximation and gives rise to a natural sequence of control variates for the ergodic average Sk(F ) = (1/k) ∑k i=1 F (Φi), where F is the force function in the Poisson equation. The main results show that the sequence...

The recently proposed L-lag coupling for unbiased Markov chain Monte Carlo (MCMC) calls a joint celebration by MCMC practitioners and theoreticians. For practitioners, it circumvents the thorny issue of deciding burn-in period or when to terminate an sampling process, opens door safe parallel implementation. theoreticians, provides powerful tool establish elegant easily estimable bounds on exac...

This paper provides an overview of the five most commonly used statistical techniques for improving the efficiency of stochastic simulations: control variates, common random numbers, importance sampling, conditional Monte Carlo, and stratification. The paper also describes a mathematical framework for discussion of efficiency issues that quantifies the trade-off between lower variance and highe...