Elicitation Complexity of Statistical Properties

A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, we instead advocate for a more nuanced question: how many dimensions are required to indirectly elicit a given property? This number is called the elicitation complexity of the property. We lay the foundation for a general theory of elicitation complexity, including several basic results about how elicitation complexity behaves, and the complexity of standard properties of interest. Building on this foundation, our main result gives tight complexity bounds for the broad class of Bayes risks. We apply these results to several properties of interest, including variance, entropy, norms, and several classes of financial risk measures. We conclude with discussion and open directions.

Predicting COVID-19 peaks around the world

The official data for the time evolution of active cases of COVID-19 pandemics around the world are available online. For all countries, a peak has been either observed (China and South Korea) or is expected in near future. The approximate dates and heights of those peaks imply in important epidemiological issues. Inspired by similar complex behaviour of volumes of transactions of stocks at NYSE and NASDAQ, we propose a q-statistical functional form which appears to describe satisfactorily the available data of all countries. Consistently, predictions become possible of the dates and heights of those peaks in severely affected countries unless efficient treatments or vaccines, or sensible modifications of the adopted epidemiological strategies, emerge.