Quantization of probability distributions under norm-based distortion measures
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چکیده
For a probability measure P on R and n∈N consider en = inf ∫ min a∈α V (‖x−a‖)dP (x) where the infimum is taken over all subsets α of R with card(α) ≤ n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n-asymptotics of en for nonsingular and for (singular) self-similar distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.
منابع مشابه
Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions
For a probability measure P on Rd and n ∈ N consider en = inf ∫ mina∈α V (‖x − a‖) dP (x) where the infimum is taken over all subsets α of Rd with card(α) n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n-asymptotics of en for self-similar distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures. ...
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تاریخ انتشار 2004