Research in Nonparametric Statistics
In order to describe the data, it is common in statistics to assume a specific probability model. Unfortunately, in many practical applications (for instance in economics, population genetics and social networks) it is not possible to identify a specific structure for the data. Nonparametric methods provide statistical tools for addressing inference in these situations.
SMSAS has an active research group in both classical and Bayesian nonparametric methods.
Areas of research
In the classical nonparametric methods, the research is focused on
- nonparametric regression, wavelets (Dr Xue Wang);
- quantile regression, local polynomial smoothing with applications to robust regression and dimension reduction, and econometrics (Dr Efang Kong); and
- spatiotemporal models, applications in neuroimaging, and finance (Prof Jian Zhang).
In the Bayesian nonparametric area, a special focus is on the construction of novel dependent priors for modelling situations where data may be divided into different groups with different densities, allowing information pooling across groups.
For example, nonparametric priors have been developed which allow inference about an unknown distribution which changes with time or some other variables. This allows time series or regression models which do not make strong assumptions and can adapt to the data.
Other research areas in Bayesian nonparametrics include
- asymptotic theory (Prof Jian Zhang);
- non-exchangeable priors, multiple hypothesis testing, and species estimation (Dr Fabrizio Leisen);
- stochastic frontier methods (Prof Jim Griffin and Dr Michalis Kolossiatis); and
- various applications in econometrics (Prof Jim Griffin, Dr Fabrizio Leisen, and Dr Michalis Kolossiatis), finance (Prof Jim Griffin and Dr Michalis Kolossiatis) and bioinformatics (Prof Jim Griffin and Dr Fabrizio Leisen).
|Prof Jim Griffin||MCMC methods for Bayesian nonparametric priors, density regression, nonparametric time series, applications in finance and economics|
|Dr Efang Kong||Empirical likelihood methods, quantile regression, local polynomial smoothing, econometrics|
|Dr Fabrizio Leisen||Dependent and non-exchangeable nonparametric priors|
|Dr Xue Wang||Wavelets, nonparametric regression|
|Prof Jian Zhang||Bayesian nonparametric asymptotics, spatiotemporal modelling, neuroimaging, finance|