Bartlett, PeterLinder, TamasLugosi, GáborUniversitat Pompeu Fabra. Departament d'Economia i Empresa2020-05-252020-05-251997-01-01IEEE Transactions on Information Theory, 44, (1998), pp. 1802-1813http://hdl.handle.net/10230/743We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers. We show that the mean squared distortion of a vector quantizer designed from $n$ i.i.d. data points using any design algorithm is at least $\Omega (n^{-1/2})$ away from the optimal distortion for some distribution on a bounded subset of ${\cal R}^d$. Together with existing upper bounds this result shows that the minimax distortion redundancy for empirical quantizer design, as a function of the size of the training data, is asymptotically on the order of $n^{1/2}$. We also derive a new upper bound for the performance of the empirically optimal quantizer.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPaperestimationhypothesis testingstatistical decision theory: operations researchStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess