| Semiparametric statistical models are indexed by an infinite-dimensional ``nuisance parameter'' and a finite-dimensional ``parameter of interest''. Although there are still many unsolved problems, a general theory of inference for semiparametric models was developed during the 1980/90s. In this theory the infinite-dimensional parameter is typically restricted to a relatively small (even though infinite-dimensional) set. This ensures existence of estimators of the parameter of interest with a precision of the order the inverse of the root of the number of observations. Typically such estimators have similar behaviour (such as asymptotic normality) as corresponding estimators in finite-dimensional models. However, in practice an a-priorirestriction of an infinite-dimensional parameter to a small set is a leap of faith and it is counter the general philosophy of semiparametric modelling not to impose unknown and uncheckable assumptions. In this project we investigate what happens in ``big'' semiparametric models. This requires both an understanding of the precision that is possible, and the development of new methods of estimation. For the latter we target both higher order estimating equations and Bayesian approaches. |
