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Model selection for regression on a random design

Yannick Baraud (2002)

ESAIM: Probability and Statistics

We consider the problem of estimating an unknown regression function when the design is random with values in k . 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....

Model selection for regression on a random design

Yannick Baraud (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating an unknown regression function when the design is random with values in k . 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...

Modifications of the double arrow space and related Banach spaces C(K)

Witold Marciszewski (2008)

Studia Mathematica

We consider the class of compact spaces K A which are modifications of the well known double arrow space. The space K A 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 K A spaces and on the isomorphic classification of the Banach spaces C ( K A ) .

Modular inequalities for the Hardy averaging operator

Hans P. Heinig (1999)

Mathematica Bohemica

If P 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 φ . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.

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