Increased Statistical Efficiency in a Lognormal Mean Model

Table 1

Relative efficiencies of SHEN₍₂₀₀₆₎ and GS₍₂₀₁₄₎ estimators across varying sample sizes and population standard deviations.

Sample size; Estimators	Relative efficiency versus the usual estimator, UER [in %]
	Population standard deviation
	𝜇=0.30	𝜇=0.35	𝜇=0.40	𝜇= 0.45	𝜇=0.50	𝜇=0.55	𝜇= 0.60
𝑛=31
SHEN(2006)	108.14	108.06	107.89	107.39	108.71	108.11	108.60
GS(2014)	129.47	125.70	123.76	119.88	117.23	113.86	112.19
𝑛=41
SHEN(2006)	106.89	106.38	106.10	105.29	106.84	105.52	106.10
GS(2014)	126.19	123.80	118.30	113.86	112.55	108.98	108.00
𝑛=51
SHEN(2006)	104.79	104.36	104.38	104.58	104.40	104.57	104.70
GS(2014)	124.74	118.70	114.05	110.72	108.10	106.59	105.63
𝑛=61
SHEN(2006)	104.25	104.29	103.85	104.26	104.57	103.93	103.43
GS(2014)	120.78	115.46	111.35	108.80	107.33	105.20	103.76
𝑛=71
SHEN(2006)	103.20	103.49	104.04	103.50	103.32	103.27	103.32
GS(2014)	117.87	112.91	110.03	107.06	105.23	104.06	103.33
𝑛=81
SHEN(2006)	103.51	103.75	102.76	102.93	102.70	103.08	103.08
GS(2014)	115.47	111.51	107.52	105.69	104.00	103.53	102.96
𝑛=91
SHEN(2006)	103.02	102.89	102.83	102.69	102.20	103.09	103.02
GS(2014)	113.48	109.63	106.91	104.88	103.11	103.39	102.80
𝑛=101
SHEN(2006)	102.53	102.27	102.41	102.30	102.65	102.40	102.27
GS(2014)	111.65	108.05	105.76	104.03	103.43	102.46	101.86
𝑛=121
SHEN(2006)	101.87	101.54	102.37	102.29	102.07	101.75	101.94
GS(2014)	109.28	105.84	104.93	103.60	102.44	101.49	101.45
𝑛=151
SHEN(2006)	101.58	102.15	102.03	101.67	101.84	101.55	101.72
GS(2014)	107.08	105.40	103.83	102.39	102.04	101.25	101.25
𝑛=201
SHEN(2006)	101.11	101.33	101.29	101.10	101.18	101.05	101.28
GS(2014)	104.82	103.39	102.28	101.38	101.08	100.64	100.83

SHEN₍₂₀₀₆₎: Shen et al. (2006) [4] estimator; GS₍₂₀₁₄₎: proposed estimator; UER: usual maximum likelihood estimator; 𝑛: sample size; 𝜇: population standard deviation.