Quasi-likelihood nonlinear models (QLNM) include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation (MQLE) ...Quasi-likelihood nonlinear models (QLNM) include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation (MQLE) is obtained in QLNM. In an important case, this rate is O(n-^1/2(loglogn)^1/2), which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.展开更多
A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvat...A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.展开更多
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) w...This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors.展开更多
This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation (MQLE) in quasi-likelihood nonlinear models ...This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation (MQLE) in quasi-likelihood nonlinear models (QLNM). Our results may be regarded as a further generalization of the relevant results in Ref. [4].展开更多
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=...In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.展开更多
In a generalized linear model with q × 1 responses, bounded and fixed p × qregressors Zi and general link function, under the most general assumption on the mini-mum eigenvalue of∑ni=1n ZiZ'i, the mome...In a generalized linear model with q × 1 responses, bounded and fixed p × qregressors Zi and general link function, under the most general assumption on the mini-mum eigenvalue of∑ni=1n ZiZ'i, the moment condition on responses as weak as possibleand other mild regular conditions, we prove that with probability one, the quasi-likelihoodequation has a solutionβn for all large sample size n, which converges to the true regres-sion parameterβo. This result is an essential improvement over the relevant results in literature.展开更多
In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood...In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.展开更多
This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the...This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.展开更多
In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem...In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.展开更多
基金Supported by the National Natural Sciences Foundation of China (10761011)Mathematical Tianyuan Fund of National Natural Science Fundation of China(10626048)
文摘Quasi-likelihood nonlinear models (QLNM) include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation (MQLE) is obtained in QLNM. In an important case, this rate is O(n-^1/2(loglogn)^1/2), which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.
基金The project supported by NSFC!(19631040)NSFJ!(BK99002)
文摘A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.
基金Supported by National Natural Science Foundation of China (No. 10761011,10671139,10901135)Natural Science Foundation of Yunnan Province(No. 2008CD081)Special Foundation for Middle and Young Excellent Teachers of Yunnan University
文摘This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors.
基金the Natural Science Foundation of Yunnan University (No. 2005Z007C) the Scientific Research Fund of Yunnan Provincial Education Department (No. 5Y0062A)+1 种基金 Mathematical Tianyuan Fund of National Natural Science Foundation of China (No. 10626048) Special Foundation for Middle and Young Excellent Teachers of Yunnan University.
文摘This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation (MQLE) in quasi-likelihood nonlinear models (QLNM). Our results may be regarded as a further generalization of the relevant results in Ref. [4].
基金supported by the National Natural Science Foundation of China(Grant No.10471136)Ph.D.Program Foundation of Ministry of Education of China and Special Foundation of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10171094&10471136)Ph.D.Program Foundation of Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q × 1 responses, bounded and fixed p × qregressors Zi and general link function, under the most general assumption on the mini-mum eigenvalue of∑ni=1n ZiZ'i, the moment condition on responses as weak as possibleand other mild regular conditions, we prove that with probability one, the quasi-likelihoodequation has a solutionβn for all large sample size n, which converges to the true regres-sion parameterβo. This result is an essential improvement over the relevant results in literature.
文摘In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.
文摘This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.
基金the National Natural Science Foundation of China under Grant Nos.10171094,10571001,and 30572285the Foundation of Nanjing Normal University under Grant No.2005101XGQ2B84+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No.07KJD110093the Foundation of Anhui University under Grant No.02203105
文摘在有固定设计的概括线性模型,在假设和另外的整齐条件下面,最大的伪可能性评估者的 asymptotic 规度,是有自然连接功能的伪可能性方程的根,被获得,在的地方表示最小的特征值, X <SUB > i </SUB >是围住的p ×& #8201 ; q 退回 ors ,和 y <SUB > i </SUB >是q ×& #8201 ; 1 回答。
基金supported by Major Programm of Natural Science Foundation of China under Grant No.71690242the Natural Science Foundation of China under Grant No.11471252the National Social Science Fund of China under Grant No.18BTJ040
基金Project supported by the National Natural Science Foundation of China (No.10371059, No.10171051).
文摘In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.
基金国家自然科学基金面上项目“金融高频大数据下的风险推断及其与多元标的衍生品定价和金融风险管理的交叉融合研究”(71871132)国家自然科学基金委重大研究计划重点项目“金融大数据统计推断理论与方法及应用研究”(91546202)+1 种基金中央高校基本科研业务费(批准号:CXJJ-2019-412)专项资金资助部分受到上海市数据科技与决策前沿科学研究基地(Shanghai Research Center for Data Science and Decision Technology)资助。