On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection

This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised nonparametric change point detection (CPD) problem. We show that the soft rank energy enjoys both fast rates of statistical convergence and robust continuity properties which lead to strong performance on real datasets. Our theoretical analyses remove the need for resampling and out-of-sample extensions previously required to obtain such rates. In contrast the rank energy suffers from the curse of dimensionality in statistical estimation and moreover can signal a change point from arbitrarily small perturbations, which leads to a high rate of false alarms in CPD. Additionally, under mild regularity conditions, we quantify the discrepancy between soft rank energy and rank energy in terms of the regularization parameter. Finally, we show our approach performs favorably in numerical experiments compared to several other optimal transport-based methods as well as maximum mean discrepancy.Comment: 36 pages, 5 figure

Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency

Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance

A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements

Multipath propagation causes major impairments to Global Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step