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A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...
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...
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