The Statistics Group’s research covers high-dimensional statistical and causal inference.

### High-dimensional statistics and robust M-estimators

Recent work in this area includes:

• asymptotic performance and hypothesis testing for regularized M-estimators via approximate message passing
• factor augmentation for sparse high-dimensional models incorporating clustering effects of covariates and hidden confounders
• marginal treatment effect estimation and inference; asymptotic property of the convolutional neural network
• conditional independence tests for large scale datasets.

### Copula models and methods

Multivariate/longitudinal response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences.

Data from these application areas have different dependence structures including features such as tail dependence.

Studying dependence among multivariate response data is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution.

When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand, one may create multivariate distributions based on particular assumptions, limiting thus their use. For example, most existing models assume rigid margins of the same form (e.g., Gaussian, Student, exponential, Gamma, Poisson, etc.) or limited dependence (e.g., tail independence, positive dependence, etc.).

To solve this problem, we use copulas (multivariate distributions with uniform margins). Copulas are unified way to model multivariate response data, as they account for the dependence structure and provide a flexible representation of the multivariate distribution. They allow for general dependence modelling, which is different from assuming simple linear correlation structures and normality. That makes them particularly well suited to the aforementioned application areas.

Specific situations where we have made use of copulas include:

1. models and inference procedures for repeated measures or multivariate discrete (binary, ordinal, count) response in biostatistical, environmental and econometrical applications
2. factor copula models for survey data
3. vine copula-GARCH models for financial returns
4. copula-mixed models for meta-analysis of diagnostic test accuracy studies.