Empirical Likelihood Confidence Region for Parameters in Semi-linear Errors-in-Variables Models

Authors: CUI, HENGJIAN; KONG, EFANG

Source: Scandinavian Journal of Statistics, Volume 33, Number 1, March 2006 , pp. 153-168(16)

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Abstract:

This paper proposes a constrained empirical likelihood confidence region for a parameter in the semi-linear errors-in-variables model. The confidence region is constructed by combining the score function corresponding to the squared orthogonal distance with a constraint on the parameter, and it overcomes that the solution of limiting mean estimation equations is not unique. It is shown that the empirical log likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the proposed confidence region has coverage probability which is closer to the nominal level, as well as narrower than those of normal approximation of generalized least squares estimator in most cases. A real data example is given.

Keywords: confidence regions; coverage probability; errors-in-variables; empirical likelihood ratio; interval length

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2006.00468.x

Publication date: 2006-03-01