Efficient and Robust Estimation for Financial Returns: An Approach Based on q-Entropy

We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvat-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and efficiency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.