Universal L^s -rate-optimality of L^r-optimal quantizers by dilatation and contraction
| dc.creator | Sagna, Abass | |
| dc.date | 2007-07-12 | |
| dc.date | 2007-11-19 | |
| dc.date.accessioned | 2026-07-07T08:43:17Z | |
| dc.date.available | 2026-07-07T08:43:17Z | |
| dc.description | Let $ r, s>0 $. For a given probability measure $P$ on $\mathbb{R}^d$, let $(α_n)_{n \geq 1}$ be a sequence of (asymptotically) $L^r(P)$- optimal quantizers. For all $μ\in \mathbb{R}^d $ and for every $θ>0$, one defines the sequence $(α_n^{θ, μ})_{n \geq 1}$ by : $\forall n \geq 1, α_n^{θ, μ} = μ+ θ(α_n - μ) = \{μ+ θ(a- μ), a \in α_n \} $. In this paper, we are interested in the asymptotics of the $L^s$-quantization error induced by the sequence $(α_n^{θ, μ})_{n \geq 1}$. We show that for a wide family of distributions, the sequence $(α_n^{θ, μ})_{n \geq 1}$ is $L^s$-rate-optimal. For the Gaussian and the exponential distributions, one shows how to choose the parameter $θ$ such that $(α_n^{θ, μ})_{n \geq 1}$ satisfies the empirical measure theorem and probably be asymptotically $L^s$-optimal. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0707.1808 | |
| dc.identifier | http://arxiv.org/abs/0707.1808 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142258 | |
| dc.subject | Probability | |
| dc.title | Universal L^s -rate-optimality of L^r-optimal quantizers by dilatation and contraction | |
| dc.type | text |