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Masterclass for the Master of Mathematical Sciences
Presented by Dr Michael Stewart, Senior Lecturer, School of Mathematics and Statistics

Join us online to experience one of the classes that may form your future course. Masterclasses are your opportunity to join a class from the actual course curriculum, delivered by a leading academic from the program.

Class topic: When infinitely many nuisance parameters are no nuisance at all
Classical statistical models are typically parametric in that they depend on a small number of parameters which need to be estimated from the data; the parameter(s) of interest can be more difficult to estimate in the presence of other unknown “nuisance” parameters. While amenable to thorough theoretical analysis, such models are often too restrictive for modern applications. Nonparametric models greatly reduce these restrictions by only assuming the distribution of the data is in some smooth function space, however the greatly increased flexibility comes with increased complexity in terms of both practial implementation and theoretical analysis.

Semiparametric models lie somewhere between where we may have a small number of parameters of interest as well as nuisance functions, effectively infinitely many nuisance parameters. A powerful theory utilising various geometric concepts including projections in Hilbert space can be used to determine “optimal” procedures in these models. We give a brief overview of the main ideas and present some curious examples: one where the much maligned “sign test” is actually optimal and another where it is possible to estimate a location parameter just as well in the presence of infinitely many unknown nuisance parameters as in the case where they are known.

This masterclass is delivered as part of STAT5610 Advanced Inference - a unit of study offered through the Master of Mathematical Sciences.

Nov 11, 2020 06:30 PM in Canberra, Melbourne, Sydney

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