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On a L1-Test Statistic of Homogeneity
Published on Feb 25, 20083913 Views
My presentation will be divided in two parts. First, I will present two simple and explicit procedures for testing homogeneity of two independent multivariate samples of size $n$. The nonparametric te
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Chapter list
On a L1-test statistic of homogeneity00:00
Outline00:31
1. A L1-test statistic for the two sample problem00:44
The problem - 100:47
The problem - 201:06
The problem - 301:18
The test statistic - 102:17
The test statistic - 203:05
Asymptotic behavior of Ln03:53
Asymptotic behavior of Tn - 104:42
Asymptotic behavior of Tn - 205:07
Asymptotic behavior of Tn - 305:18
Asymptotic behavior of Tn - 405:27
Rate functions gL and gT05:36
Sketch of proof - 106:30
Sketch of proof - 206:51
Sketch of proof - 307:16
Sketch of proof - 407:52
Sketch of proof - 507:58
Sketch of proof - 608:11
Sketch of proof - 708:25
A distribution-free strong consistent test - 109:01
A distribution-free strong consistent test - 209:23
A distribution-free strong consistent test - 309:31
A strong consistent test - Corollary10:15
Asymptotic normality - 111:29
Asymptotic normality - 211:48
Asymptotic normality - Theorem12:09
Sketch of proof - 112:41
Sketch of proof - 212:56
rSketch of proof - 313:11
Sketch of proof - 413:25
Sketch of proof - 513:48
Sketch of proof - 614:26
Sketch of proof - 714:38
Proposition14:45
A consistent test - Corollary15:57
2. Application to density model selection16:49
The problem - 116:54
The problem - 217:27
Objective - 117:42
Objective - 218:04
Objective - 318:27
Objective - 418:35
Examples I - 118:55
Examples I - 219:36
Examples I - 319:41
Examples I - 419:43
Examples I - 519:45
Examples II - 119:58
Examples II - 220:12
Examples II - 320:28
Examples II - 420:43
A closure condition - 121:16
A closure condition - 221:48
A closure condition - 321:58
Complexity estimation - 122:33
Complexity estimation - 222:44
Complexity estimation - 322:52
Complexity estimation - 423:50
Complexity estimation - 524:04
Complexity estimation - Theorem24:17
Fast density estimate - 125:01
Fast density estimate - 226:34
Fast density estimate - 326:59
Fast density estimate - 428:18
Fast density estimate - 528:35
Link with the VC theory - 129:12
Link with the VC theory - 229:35
Link with the VC theory - 329:49
Discussion - 130:05
Discussion - 230:16
Discussion - 330:24
On the closure condition - 130:49
On the closure condition - 231:28
The mixture case - 132:35
The mixture case - 233:13