Robust estimation of superhedging prices

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. We establish consistency and robustness of these estimators and argue that they offer a superior performance relative to the plugin estimator. We generalise the results by replacing the superhedging criterion with acceptance relative to a risk measure. We further extend our study, in part, to the case of markets with traded options, to a multiperiod setting and to settings with model uncertainty. We also study convergence rates of estimators and convergence of superhedging strategies.Comment: This work will appear in the Annals of Statistics. The above version merges the main paper to appear in print and its online supplemen

Robust estimation for ARMA models

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard M-estimates and to estimates based on a diagnostic procedure.Comment: Published in at http://dx.doi.org/10.1214/07-AOS570 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust estimation in simultaneous equations models

In this paper we review existing work on robust estimation for simultaneous equations models. Then we discuss three strategies for obtaining estimators with a high breakdown point, a controllable efficiency, and a reasonable computational cost: (a) robustifying Three-Stages Least Squares, (b) robustifying the Full Information Maximum Likelihood method by minimizing the determinant of a robust covariance matrix of residuals, and (c) generalizing multivariate tauestimators (Lopuhaa 1991) to these models. The latter seems the most promising approach

Robust estimation for ordinal regression.

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.Breakdown point; Diagnostic plot; Influence function; Ordinal regression; Weighted maximum likelihood; Robust distances;

Robust Estimation for Linear Panel Data Models

In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. However, when the ordinary least squares (OLS) method is used to estimate the model parameters, presence of outliers may significantly alter the adequacy of such models by producing biased and inefficient estimates. In this work we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure data set. Our thorough study demonstrates that the proposed estimators show significantly better performances over the traditional methods in the presence of outliers and produce competitive results to the OLS based estimates when no outliers are present in the data set