Distortion mismatch in the quantization of probability measures

Siegfried Graf; Harald Luschgy; Gilles Pagès

Displaying similar documents to “Distortion mismatch in the quantization of probability measures”

Generalized quasilinearization method and higher order of convergence for second-order boundary value problems.

Melton, Tanya G., Vatsala, A.S. (2006)

Boundary Value Problems [electronic only]

Similarity:

On some BK spaces.

De Malafosse, Bruno (2003)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Universal -rate-optimality of -optimal quantizers by dilatation and contraction

Abass Sagna (2009)

ESAIM: Probability and Statistics

Similarity:

We investigate in this paper the properties of some dilatations or contractions of a sequence ( of -optimal quantizers of an $ℝ^{d}$ -valued random vector $X \in L^{r} (ℙ)$ defined in the probability space $(Ω, 𝒜, ℙ)$ with distribution $ℙ_{X} = P$ . To be precise, we investigate the -quantization rate of sequences $α_{n}^{θ, μ} = μ + θ (α_{n} - μ) = {μ + θ (a - μ), a \in α_{n}}$ when $θ \in ℝ_{+}^{☆}, μ \in ℝ, s \in (0, r)$ or ∈ (r, +∞) and $X \in L^{s} (ℙ)$ . We show that for a wide family of distributions, one may always find parameters (θ,µ) such that ( is -rate-optimal. For the Gaussian and the exponential distributions we show the existence...