Add to ORKGIt is shown that there are no consistent decision rules for the hypothesis testing problem of distinguishing between absolutely continuous and purely singular probability distributions on the real line. In fact, there are no consistent decision rules for distinguishing between absolutely continuous distributions and distributions supported by Borel sets of Hausdorff dimension 0. It follows that there is no consistent sequence of estimators of the Hausdorff dimension of a probability distribution.Consistent decision rule Singular measure Hausdorff dimension
The result by Dvoretzky, Wald, and Wolfowitz on the sufficiency of nonrandomized decision rules for ...
We study the task of testing properties of probability distributions and our focus is on understandi...
AbstractThe following path properties of real separable Gaussian processes ξ with parameter set an a...
It is shown that there are no consistent decision rules for the hypothesis testing problem of distin...
AbstractThe problem of the determination of the Hausdorff dimension of sets via the special class of...
Lebid M. Fractal analysis of singularly continuous measures generated by Cantor series expansions. B...
AbstractIt is shown that every full eA decomposable probability measure on Rk, where A is a linear o...
The paper is devoted to the study of connections between fractal properties of one-dimensional singu...
The paper presents a proof, using methods of the theory of distributions of the famous result of A. ...
Many non- and semi- parametric estimators have asymptotic properties that have been established unde...
The paper provides a condition for differentiability as well as an equivalent criterion for Lipschit...
We prove that every closed set which is not (sigma)-finite with respect to the Hausdorff measure (cH...
AbstractWe prove that an absolutely continuous probability distribution with compact support is unif...
The need for calculating and characterizing singular normal distributions arises in a natural way wh...
In this paper we study mutual absolute continuity, finiteness of relative entropy and the possibilit...
The result by Dvoretzky, Wald, and Wolfowitz on the sufficiency of nonrandomized decision rules for ...
We study the task of testing properties of probability distributions and our focus is on understandi...
AbstractThe following path properties of real separable Gaussian processes ξ with parameter set an a...
It is shown that there are no consistent decision rules for the hypothesis testing problem of distin...
AbstractThe problem of the determination of the Hausdorff dimension of sets via the special class of...
Lebid M. Fractal analysis of singularly continuous measures generated by Cantor series expansions. B...
AbstractIt is shown that every full eA decomposable probability measure on Rk, where A is a linear o...
The paper is devoted to the study of connections between fractal properties of one-dimensional singu...
The paper presents a proof, using methods of the theory of distributions of the famous result of A. ...
Many non- and semi- parametric estimators have asymptotic properties that have been established unde...
The paper provides a condition for differentiability as well as an equivalent criterion for Lipschit...
We prove that every closed set which is not (sigma)-finite with respect to the Hausdorff measure (cH...
AbstractWe prove that an absolutely continuous probability distribution with compact support is unif...
The need for calculating and characterizing singular normal distributions arises in a natural way wh...
In this paper we study mutual absolute continuity, finiteness of relative entropy and the possibilit...
The result by Dvoretzky, Wald, and Wolfowitz on the sufficiency of nonrandomized decision rules for ...
We study the task of testing properties of probability distributions and our focus is on understandi...
AbstractThe following path properties of real separable Gaussian processes ξ with parameter set an a...