Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood

Table 4

Empirical average interval lengths for the 95% confidence intervals for the mean using the blockwise EL method (EL) and the blockwise EL method with the Bartlett correction (EL_𝐵) for the data generated from an AR(1) process with 𝜙=0.5 and with a marginal negative binomial distribution Negbinom(𝜇,𝜃), based on 10 000 samples.

𝑛	𝑀=𝐿	𝜃=0.1		𝜃=0.5		𝜃=1.0
		EL	EL𝐵	EL	EL𝐵	EL	EL𝐵
50	2	1.62	1.70	0.85	0.88	0.65	0.68
100	2	1.47	1.54	0.68	0.71	0.51	0.52
	4	1.49	1.55	0.73	0.76	0.54	0.56
	5	1.48	1.55	0.73	0.76	0.55	0.57
200	2	1.25	1.31	0.52	0.53	0.38	0.39
	4	1.32	1.37	0.57	0.58	0.41	0.43
	5	1.31	1.36	0.58	0.59	0.42	0.44
500	2	0.97	1.02	0.34	0.35	0.25	0.25
	4	1.04	1.08	0.38	0.39	0.28	0.28
	5	1.03	1.08	0.39	0.40	0.28	0.29
	10	1.06	1.10	0.40	0.41	0.30	0.31
1000	2	0.84	0.88	0.25	0.26	0.18	0.18
	4	0.90	0.93	0.29	0.29	0.20	0.20
	5	0.91	0.95	0.29	0.30	0.20	0.21
	10	0.92	0.95	0.31	0.31	0.21	0.22
	20	0.92	0.95	0.31	0.32	0.22	0.22