Weighted Lin-Wang Tests for Crossing Hazards

Table 2

Empirical levels of the Lin-Wang test, and three weighted variants.

Sample sizes	LW	LW𝑤1	LW𝑤2	LW𝑤3
(20,20)	0.044	0.045	0.044	0.042
(30,30)	0.048	0.053	0.053	0.048
(40,40)	0.046	0.048	0.047	0.045
(50,50)	0.051	0.053	0.050	0.049
(60,60)	0.053	0.045	0.051	0.053
(70,70)	0.049	0.049	0.051	0.047
(80,80)	0.056	0.047	0.053	0.053
(90,90)	0.051	0.049	0.050	0.050
(100,100)	0.048	0.050	0.049	0.048

Notes: Sample sizes are given for group 1, followed by group 2. LW denotes the Lin-Wang test, and LW_𝑤𝑖 denotes the weighted version of the LW test, with weights 𝑤_𝑖 as described in the text. The underlying distributions of group 1 and group 2 were identical, as described in the text. The empirical levels of the two-sided test statistics were estimated from 5000 simulations, at nominal alpha level 0.05.