In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptot...In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent X 2 1 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.展开更多
基金This work was supported by the National Natural Science Foundation of China(Key Grant 10231030,Special Grant 10241001)Humboldt-Universitat Berlin-Sonderforschungsbereich 373.
文摘In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent X 2 1 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively.
