Linear ?-minimax estimators for a bounded normal mean have been explored by Vidakovic and DasGupta (1992). They have found that the risk of linear ?-minimax rules is close to the risk of exact ?-minimax rules. However, the linear rules are not very natural when one estimates bounded parameters. In this paper we explore some modiications of linear rules with two goals in mind: (i) addressing the...

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s conjectures on self-similarity and “hairiness” of the Mandelbrot set near the corresponding parame...

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s conjectures on self-similarity and “hairiness” of the Mandelbrot set near the corresponding parame...

We deal with a parametric version of timed game automata (PGA), where clocks can be compared to parameters, and parameter synthesis. As usual, parametrization leads to undecidability of the most interesting problems, such as reachability game. It is not surprising then that the symbolic exploration of the state-space often does not terminate. It is known that the undecidability remains even whe...

A parallel algorithm for detecting dominant points on a digital closed curve is presented. The procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve. The procedure first determines the region of support for each point based on its local properties, then computes measures of relative significance (e.g., curvature) of each...