Partially Adaptive and Robust Estimation of Asset Models: Accommodating Skewness and Kurtosis in Returns

Abstract

Robust regression estimation deals with selecting estimators that have desirable statistical properties when applied to data drawn from a wide range of distributional characteristics. Ideally, robust estimators are insensitive to small departures from the assumed distributions and hopefully would be unbiased and have variances close to estimators based on the true distribution. The approach explored in this paper is to select an estimator based on a flexible distribution which includes, for example, the normal as a limiting case. Thus, the corresponding estimator can accommodate normally distributed data as well as data having significant skewness and kurtosis. In the case when an assumed distribution over-parameterizes the true distribution, the variance of the estimator is larger than necessary, but often the increases are modest and much smaller than assuming a model which does not include the true distribution. The selection of a flexible probability distribution can impact the efficiency and biasedness of the corresponding robust estimator. Knowing the relations among potential distributions can lead to a better estimator that improves efficiency, avoids bias, and reduces the impact of misspecification.