2.2.2 Efficiency Plots -- 2.2.3 Practical Recommendations -- 2.3 Quantization -- 2.3.1 Bounds for Optimal Quantizers -- 2.3.2 Boundary Correction for Nearest Neighbor Distances -- 2.3.3 Approximating Quantization Error for Finite n -- Approximating Quantization Using Partial Covering -- Approximations Based on the Use of the Spherical Model -- Simulation Study -- CLT-Based Approximations for the Quantization Error -- Simulation Study -- Approximating Mean Squared Quantization Error Using Extreme Value Theory -- A Simple Approximation for Mean Squared Quantization Error -- Simulation Study -- 2.3.4 Efficient Exploration Designs for Quantization -- 2.3.5 Equivalence to the Problem of Partial Covering -- 2.4 Quantization Using the Checkerboard Lattice Points -- 2.4.1 Reformulation in Terms of the Voronoi Cells -- Re-normalization of the Quantization Error -- Voronoi Cells for Dn,δ -- 2.4.2 Explicit Formulae for the Quantization Error -- 2.4.3 Closed-Form Expressions for the Coverage Area -- Reduction to Voronoi Cells -- Expressing Fd(Dn,δ,r) Through Fd,Z(r) -- Simple Bounds for Fd(Dn,δ,r) -- Radius Required for Partial Covering Is Much Smaller than the Covering Radius -- Numerical Studies -- Quantization and Weak Covering Comparisons -- Accuracy of Covering Approximation and Dependence on δ -- Stochastic Dominance -- 2.4.4 The Checkerboard Lattice with Point at Zero -- An Auxiliary Result -- Normalised Mean Squared Quantization Error for Dn,δ,0(0) -- Quantization Error for the Design Dn,δ,0 -- Numerical Studies -- References. |