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Second Order Hadamard Differentiability in Statistical Applications
Cramer-von Mises statistic goodness of fit test Hadamard differentiability limiting distribution linear models M-estimator statistical functionals uniform asymptotic linearity weighted empirical processes
2015/12/11
A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limitin...
Regularization of statistical inverse problems and the Bakushinskii veto
statistical inverse problems the Bakushinskii veto
2010/11/22
In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statist...
Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities
Statistical properties of nonuniformly 1d maps logarithmic singularities
2010/12/13
For a certain parametrized family of maps on the circle, with critical points and
logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed...
Equi-Statistical Extension of the Korovkin Type Approximation Theorem
Equi-statistical convergence positive linear operator Korovkin type theorem
2010/2/25
In this paper using equi-statistical convergence, which is stronger than the usual uniform convergence and statistical uniform convergence, we obtain a general Korovkin type theorem. Then, we construc...