The Nonexistence of Certain Statistical Procedures in Nonparametric Problems

Nonparametric statistical inverse problems

We explain some basic theoretical issues regarding nonparametric statistics applied to inverse problems. Simple examples are used to present classical concepts such as the white noise model, risk estimation, minimax risk, model selection and optimal rates of convergence, as well as more recent concepts such as adaptive estimation, oracle inequalities, modern model selection methods, Stein’s unb...

Handbook of Parametric and Nonparametric Statistical Procedures

On the nonexistence of certain branched covers

Starting with the classical result of Alexander [1], asserting that every closed, orientable PL–manifold of dimension n admits a branched cover onto the n–dimensional sphere S , a series of authors such as Berstein and Edmonds [3], Edmonds [11], Hilden [15], Hirsch [16], Iori and Piergallini [18], Montesinos [19] and Piergallini [20] have proved the existence of branched covers satisfying certa...

The Nonexistence of Certain Tight Spherical Designs

In this paper, the nonexistence of tight spherical designs is shown in some cases left open to date. Tight spherical 5-designs may exist in dimension n = (2m + 1)2 − 2, and the existence is known only for m = 1, 2. In the paper, the existence is ruled out under a certain arithmetic condition on the integer m, satisfied by infinitely many values of m, including m = 4. Also, nonexistence is shown...

The Nonexistence of a Certain Steiner System

Although the automorphism group of a projective plane of order 10, if one exists, must be very small, such a plane could be the derived design of a Steiner system S(3, 12, 112) with a larger group. There are several reasons why the Frobenius group of order 56 is a promising candidate for the latter group. However, in this paper it is shown that there is no S(3, 12, 112) which is fixed by this F...