Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Statistics and Probability
A Resistant Estimator Of Multivariate Location And Dispersion, David J. Olive
A Resistant Estimator Of Multivariate Location And Dispersion, David J. Olive
Articles and Preprints
This paper presents a simple resistant estimator of multivariate location and dispersion. The DD plot is a plot of Mahalanobis distances from the classical estimator versus the distances from a resistant estimator and can be used to detect outliers and as a diagnostic for multivariate normality. The new estimator can be used in the DD plot, is easy to compute and provides insights about several useful robust algorithm techniques.
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan
Articles and Preprints
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.