Möbius invariant function spaces.
We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small probability....
We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small...
We consider the class of compact spaces which are modifications of the well known double arrow space. The space is obtained from a closed subset K of the unit interval [0,1] by “splitting” points from a subset A ⊂ K. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of spaces and on the isomorphic classification of the Banach spaces .
If is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form u (Pf) Cv (f) are established for a general class of functions . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.