Research Article

Empirical Likelihood for Multidimensional Linear Model with Missing Responses

Table 1

Empirical coverage probabilities of the confidence regions for 𝛽 under different selection probability functions 𝑝 ( 𝑥 ) and sample sizes 𝑛 when nominal level is 0.95.

𝑛 Case I Case II
𝑝 0 ( 𝑥 , 𝜃 1 ) 𝑝 0 ( 𝑥 , 𝜃 2 ) 𝑝 0 ( 𝑥 , 𝜃 3 ) 𝑝 1 ( 𝑥 ) 𝑝 2 ( 𝑥 ) 𝑝 3 ( 𝑥 )

100 0.554 0.61 0.571 0.861 0.772 0.693
WCEL 200 0.594 0.729 0.611 0.971 0.916 0.818
500 0.699 0.914 0.698 0.995 0.987 0.967

100 0.486 0.489 0.516 0.667 0.591 0.521
AEL 200 0.549 0.536 0.564 0.805 0.587 0.587
500 0.655 0.653 0.6600.932 0.863 0.759