Optimal Bandwidth Selection for Kernel Density Functionals Estimation
Table 1
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
.197
.154
.236
.171
.221
.163
.302
.270
.359
.298
.300
.268
1st quantile
.182
.144
.205
.156
.200
.153
.278
.254
.307
.258
.265
.243
Median
.197
.154
.233
.170
.227
.167
.301
.270
.376
.317
.300
.268
3rd quantile
.214
.163
.265
.185
.254
.183
.327
.287
.431
.355
.336
.293
Cauchy
Mean
.325
.240
.320
.222
.290
.205
.497
.422
.440
.331
.419
.338
1st quantile
.273
.214
.264
.198
.230
.174
.417
.377
.330
.265
.348
.310
Median
.316
.236
.312
.219
.295
.207
.484
.415
.455
.353
.416
.342
3rd quantile
.365
.265
.368
.245
.355
.238
.557
.465
.554
.415
.478
.387
Pareto
Mean
.442
.332
.263
.178
.145
.098
.676
.583
.207
.143
.374
.284
1st quantile
.329
.267
.210
.151
.103
.078
.502
.469
.140
.106
.298
.241
Median
.422
.320
.251
.174
.137
.091
.646
.563
.200
.131
.359
.278
3rd quantile
.519
.386
.300
.202
.174
.109
.794
.678
.260
.173
.428
.327
Mix-Normal I
Mean
.378
.289
.389
.279
.349
.253
.578
.507
.522
.413
.495
.417
1st Quantile
.360
.279
.342
.252
.282
.211
.551
.490
.389
.320
.438
.376
Median
.377
.288
.382
.273
.362
.259
.577
.506
.510
.403
.489
.407
3rd Quantile
.397
.298
.431
.309
.428
.304
.607
.524
.658
.510
.544
.460
Mix-Normal II
Mean
.342
.263
.364
.255
.322
.227
.522
.461
.492
.372
.467
.389
1st Quantile
.321
.251
.318
.229
.254
.188
.490
.441
.339
.279
.413
.347
Median
.342
.262
.361
.254
.345
.231
.523
.461
.509
.355
.464
.387
3rd Quantile
.364
.274
.403
.278
.397
.275
.556
.481
.642
.461
.519
.425
ROT bandwidth for estimation of given by (12); 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].
