Limit Theorems for Multi-dimensional Random Quan- Tizers
نویسنده
چکیده
We consider the r th power quantization error arising in the optimal approximation of a d-dimensional probability measure P by a discrete measure supported by the realization of n i.i.d. random variables X1, ...,Xn. For all d ≥ 1 and r ∈ (0,∞) we establish mean and variance asymptotics as well as central limit theorems for the r th power quantization error. Limiting means and variances are expressed in terms of the densities of P and X1. Similar convergence results hold for the random point measures arising by placing at each X i , 1≤ i ≤ n, a mass equal to the local distortion.
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