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

Table 3

Empirical coverage accuracy 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	0.630	0.655	0.759	0.772	0.808	0.825
100	2	0.671	0.698	0.783	0.791	0.830	0.837
	4	0.674	0.697	0.797	0.808	0.839	0.852
	5	0.658	0.679	0.793	0.802	0.839	0.859
200	2	0.686	0.693	0.805	0.815	0.835	0.839
	4	0.692	0.714	0.826	0.833	0.859	0.867
	5	0.684	0.706	0.833	0.845	0.866	0.877
500	2	0.678	0.693	0.832	0.838	0.882	0.886
	4	0.710	0.719	0.858	0.872	0.912	0.915
	5	0.706	0.712	0.870	0.883	0.920	0.921
	10	0.714	0.730	0.881	0.894	0.919	0.927
1000	2	0.724	0.735	0.827	0.836	0.871	0.875
	4	0.746	0.757	0.871	0.877	0.902	0.907
	5	0.751	0.762	0.869	0.872	0.909	0.913
	10	0.749	0.765	0.878	0.887	0.923	0.926
	20	0.749	0.770	0.882	0.897	0.924	0.932