Optimal Bandwidth Selection for Kernel Density Functionals Estimation
Table 2
Optimal bandwidth selection in estimation of with comparison to classical bandwidth selection methods.
Bandwidth selection for estimation of
Proposed method
Classical bandwidth for KDE
100
100
100
100
100
100
Normal
Mean
.086
.067
.236
.173
.221
.163
.303
.271
.358
.298
.300
.270
1st quantile
.079
.063
.203
.156
.198
.150
.278
.256
.296
.256
.263
.244
Median
.086
.067
.236
.173
.229
.170
.304
.272
.380
.320
.302
.272
3rd quantile
.094
.071
.267
.190
.254
.185
.329
.287
.432
.361
.334
.296
Cauchy
Mean
.137
.104
.312
.221
.283
.200
.488
.422
.428
.320
.410
.337
1st quantile
.114
.092
.258
.194
.223
.164
.406
.373
.317
.238
.342
.298
Median
.136
.103
.304
.217
.285
.201
.483
.416
.431
.335
.405
.339
3rd quantile
.157
.115
.359
.244
.347
.236
.554
.468
.548
.414
.475
.387
Pareto
Mean
.191
.147
.276
.188
.145
.099
.673
.595
.201
.143
.372
.290
1st quantile
.142
.122
.216
.163
.107
.076
.501
.495
.140
.106
.296
.254
Median
.180
.142
.263
.185
.138
.093
.635
.574
.193
.128
.357
.285
3rd quantile
.219
.166
.318
.208
.173
.114
.775
.673
.245
.174
.430
.322
Mix-Normal I
Mean
.146
.112
.566
.369
.508
.342
.578
.507
.551
.417
.505
.420
1st quantile
.140
.109
.398
.289
.352
.254
.549
.490
.390
.332
.440
.378
Median
.147
.112
.481
.334
.454
.316
.577
.507
.549
.407
.500
.414
3rd quantile
.154
.116
.634
.391
.593
.382
.608
.523
.719
.500
.563
.458
Mix-Normal II
Mean
.103
.080
.442
.272
.442
.247
.521
.461
.489
.359
.465
.387
1st quantile
.094
.076
.310
.220
.258
.173
.491
.443
.341
.257
.412
.348
Median
.106
.081
.363
.246
.350
.226
.522
.458
.490
.353
.461
.382
3rd quantile
.114
.087
.468
.282
.470
.278
.555
.481
.637
.456
.514
.419
ROT bandwidth for estimation of given by (16); 2DPI bandwidth for estimation of with pilot bandwidth ; 3DPI bandwidth for estimation of with pilot bandwidth ; 4ROT bandwidth for density estimation proposed in Silverman [7]; 5LSCV bandwidth for density estimation proposed in Bowman [8]; 6DPI bandwidth for density estimation proposed in Sheather and Jones [9].
