Analysis of Multi-Index Monte Carlo Estimators for a Zakai SPDE

Monte Carlo Analysis of Change Point Estimators

We consider several estimators for the change point in a sequence of independent observations. These are defined as the maximizing points of usually used statistics for nonparametric change point detection problems. Our investigations focus on the non asymptotic behaviour of the proposed estimators for sample sizes commonly observed in practice. We conducted a broad Monte Carlo study to compare...

Analysis of Estimators for Adaptive Kinetic Monte Carlo

Nonlinear Monte Carlo Estimators for Parabolic Equation

We consider the parabolic type equation with a source-sink term and construct the Monte Carlo estimator for it. The procedure is based on the Hopf-Cole transformation and a Monte Carlo estimator for the correspondent Burgers equation. Monte Carlo estimators for the heat and diffusion equations are very well known since the first steps of the method. The algorithms are based usually on the intim...

Efficient Combination of Partial Monte Carlo Estimators

In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this technical report, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion...

Robust estimation of the Pareto index: A Monte Carlo Analysis

The Pareto distribution is often used in many areas of economics to model the right tail of heavytailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution– the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years...