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

Table 1

Empirical coverage accuracy for 95% confidence intervals for the mean using different methods for the iid data generated with a marginal negative binomial distribution Negbinom(𝜇,𝜃), based on 10 000 samples.

	𝑛	𝑡	EL	EL𝐵	EL𝐹	EL𝐹𝐵	𝐵perc	𝐵norm	𝐵basic	𝐵stud	𝐵bn	𝐵ubn
𝜃=0.1	20	0.797	0.808	0.821	0.829	0.840	0.797	0.783	0.744	0.926	0.898	0.889
	50	0.848	0.884	0.898	0.897	0.902	0.861	0.837	0.807	0.945	0.961	0.944
	100	0.889	0.917	0.924	0.922	0.928	0.907	0.888	0.856	0.948	0.979	0.966
𝜃=0.5	20	0.893	0.890	0.901	0.905	0.918	0.881	0.874	0.853	0.943	0.980	0.965
	50	0.916	0.921	0.928	0.929	0.932	0.916	0.910	0.906	0.945	0.993	0.980
	100	0.937	0.947	0.950	0.950	0.952	0.936	0.929	0.920	0.955	0.998	0.995
𝜃=1.0	20	0.918	0.905	0.914	0.920	0.931	0.900	0.902	0.894	0.940	0.985	0.972
	50	0.931	0.934	0.940	0.939	0.944	0.931	0.924	0.919	0.947	0.995	0.985
	100	0.941	0.946	0.948	0.950	0.952	0.936	0.936	0.936	0.955	0.995	0.990