One of the oldest problems in data stream model is to approximate p th moment \(\Vert \mathbf {X}\Vert _p^p = \sum _{i=1}^n {X}_i^p\) an underlying non-negative vector \(\mathbf {X}\in \mathbb {R}^n\) , which presented as a sequence \(\mathrm{poly}(n)\) updates its coordinates. Of particular interest when \(p \in (0,2]\) . Although tight space bound \(\Theta (\epsilon ^{-2} \log n)\) bits known...

A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic efficiency of a distributed estimation algorithm that uses constant modulus transmissions over Gaussian multiple access channels. The loss in efficiency of th...