Two-sample extended empirical likelihood for estimating equations. (English) Zbl 1327.62312
Summary: We propose a two-sample extended empirical likelihood for inference on the difference between two \(p\)-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett correctable but its domain is a bounded subset of the parameter space. We expand its domain through a composite similarity transformation to derive the two-sample extended empirical likelihood which is defined on the full parameter space. The extended empirical likelihood has the same asymptotic distribution as the standard one and can also achieve the second-order accuracy of the Bartlett correction. We include two applications to illustrate the use of two-sample empirical likelihood methods and to demonstrate the superior coverage accuracy of the extended empirical likelihood confidence regions.
MSC:
| 62G20 | Asymptotic properties of nonparametric inference |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
Bartlett correction; composite similarity transformation; extended empirical likelihood; estimating equation; similarity transformation; two-sample empirical likelihoodReferences:
| [2] | Chen, S. X.; Cui, H. J., On the second-order properties of empirical likelihood with moment restrictions, J. Econometrics, 141, 492-516 (2007) · Zbl 1407.62157 |
| [3] | Chen, Wen-Hao, Cross-national differences in income mobility: Evidence from Canada, the United States, Great Britain and Germany, Rev. Income Wealth, 55, 1, 75-100 (2009) |
| [4] | DiCicciof, T. J.; Hall, P.; Romano, J. P., Bartlett adjustment for empirical likelihood. Technical Report 298 (1988), Dept. Statistics, Stanford Univ.: Dept. Statistics, Stanford Univ. Stanford, California |
| [5] | DiCiccio, T. J.; Hall, P.; Romano, J. P., Empirical likelihood is Bartlett correctable, Ann. Statist., 19, 1053-1061 (1991) · Zbl 0725.62042 |
| [6] | Domeij, David; Flodén, Martin, Inequality trends in Sweden 1978-2004, Rev. Econ. Dynam., 13, 1, 179-208 (2010) |
| [7] | Gini, C., On the measure of concentration with special reference to income and statistics, (General Series, vol. 208 (1936), Colorado College Publication), 73-79 |
| [8] | Hall, P.; La Scala, B., Methodology and algorithm of empirical likelihood, Internat. Statist. Rev., 58, 109-127 (1990) · Zbl 0716.62003 |
| [9] | Jing, B. Y., Two-sample empirical likelihood method, Statist. Probab. Lett., 24, 315-319 (1995) · Zbl 0837.62039 |
| [10] | Liu, Y.; Chen, J., Adjusted empirical likelihood with high-order precision, Ann. Statist., 38, 1341-1362 (2010) · Zbl 1189.62054 |
| [11] | Liu, Y. K.; Yu, C. W., Bartlett correctable two-sample adjusted empirical likelihood, J. Multivariate Anal., 101, 1701-1711 (2010) · Zbl 1189.62084 |
| [12] | Liu, Y. K.; Zou, C. L.; Zhang, R. C., Empirical likelihood for two-sample mean problem, Statist. Probab. Lett., 78, 548-556 (2008) · Zbl 1136.62331 |
| [13] | Owen, A. B., Empirical likelihood ratio confidence regions for single functional, Biometrika, 75, 237-249 (1988) · Zbl 0641.62032 |
| [14] | Owen, A. B., Empirical likelihood confidence regions, Ann. Statist., 18, 90-120 (1990) · Zbl 0712.62040 |
| [15] | Owen, A. B., Empirical Likelihood (2001), Chapman & Hall/CRC: Chapman & Hall/CRC London · Zbl 0989.62019 |
| [16] | Peng, Liang, Empirical likelihood methods for the Gini index, Aust. N. Z. J. Stat., 53, 2, 131-139 (2011) · Zbl 1241.91101 |
| [17] | Qin, J.; Lawless, J., Empirical likelihood and general estimating equations, Ann. Statist., 22, 300-325 (1994) · Zbl 0799.62049 |
| [18] | Qin, Yongsong; Rao, J. N.K.; Wu, Changbao, Empirical likelihood confidence intervals for the Gini measure of income inequality, Ecol. Modell., 27, 1429-1435 (2010) |
| [19] | Qin, Y.; Zhao, L., Empirical likelihood ratio confidence intervals for various differences of two populations, J. Systems Sci. Math. Sci., 13, 23-30 (2000) · Zbl 0973.62038 |
| [20] | Tsao, M., Extending the empirical likelihood by domain expansion, Canad. J. Statist., 41, 257-274 (2013) · Zbl 1273.62076 |
| [21] | Tsao, M.; Wu, F., Empirical likelihood on the full parameter space, Ann. Statist., 41, 2176-2196 (2013) · Zbl 1360.62140 |
| [22] | Tsao, M.; Wu, F., Extended empirical likelihood for estimating equations, Biometrika, 101, 703-710 (2014) · Zbl 1334.62044 |
| [23] | Wu, F.; Tsao, M., Two-sample extended empirical likelihood, Statist. Probab. Lett., 84, 81-87 (2013) · Zbl 1407.62159 |
| [24] | Wu, C.; Yan, Y., Empirical likelihood inference for two-sample problems, Stat. Interface, 5, 345-354 (2012) · Zbl 1383.62137 |
| [25] | Zi, X. M.; Zou, C. L.; Liu, Y. K., Two-sample empirical likelihood method for difference between coefficients in linear regression model, Statist. Papers, 53, 1, 83-93 (2012), Springer · Zbl 1241.62038 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
