Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected ...Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.展开更多
Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in t...Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations EFG(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semiparametric estimating equations are developed, and the corresponding Wilk's theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11301569,11471029 and 11101014)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)Hong Kong Research Grant(Grant No.HKBU202711)Hong Kong Baptist University FRG Grants(Grant Nos.FRG2/11-12/110 and FRG1/13-14/018)
文摘Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.
基金supported partly by National Natural Science Foundation of China (Grant Nos. 11071022, 11028103 and 11201317)Key Project of Ministry of Education of China (Grant No. 309007)National High-tech R&D Program of China (Grant No. 2008AA12Z107)
文摘Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations EFG(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semiparametric estimating equations are developed, and the corresponding Wilk's theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented.
