Learning and inference from survey data

My research aims to draw reliable conclusions from data collected through surveys. I am interested both in finite population quantities, such as totals, means or quantiles, and in superpopulation quantities, such as a regression function. This work is organized around four themes, described below: machine learning for finite population inference, statistical learning from survey data, missing data and high-dimensional inference.

Surveys remain the backbone of official statistics, from employment figures to health and economic indicators. They increasingly have to deliver reliable estimates in difficult settings: falling response rates, many auxiliary variables, highly nonlinear relationships, or domains containing few sampled units (small area estimation). Combining surveys with other sources of data (data integration) adds further challenges. In such settings, classical procedures may lose some of their properties, and newer ones, including methods from statistical learning, raise new questions.

Survey data add a further difficulty: they are often neither independent nor identically distributed. Units are typically drawn without replacement, which creates dependence. They are often selected with unequal probabilities, so that observations are not identically distributed, and the sampling design can even be informative. Classical survey theory was built to handle these features. Many of the newer methodologies, such as machine learning, were instead developed for independent and identically distributed data. They offer new ways to address classical survey problems, as well as emerging ones, provided that both the methods and their theory are adapted to the sampling design.

My aim is to understand and improve current methodologies in these settings: to derive the asymptotic properties of estimators, to quantify their uncertainty, and to identify when they are optimal.