Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asympt...Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.展开更多
This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A na...This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A natural method is the averaging divide-and-conquer approach,which splits data into several blocks,obtains the estimators for each block and then aggregates the estimators via averaging.However,there is a restriction on the number of blocks.To overcome this limitation,this paper proposed a computationally efficient method,which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations.The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks.We present both theoretical analysis and experiments to explore the property of the proposed method.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871072)Natural Science Foundation of Shanxi Province of China (Grant No. 2007011014)PhD Program Scholarship Fund of ECNU 2009
文摘Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.
基金the Fundamental Research Funds for the Central Universities of China(No.2232020D-43).
文摘This paper studies the inference problem of index coefficient in single-index models under massive dataset.Analysis of massive dataset is challenging owing to formidable computational costs or memory requirements.A natural method is the averaging divide-and-conquer approach,which splits data into several blocks,obtains the estimators for each block and then aggregates the estimators via averaging.However,there is a restriction on the number of blocks.To overcome this limitation,this paper proposed a computationally efficient method,which only requires an initial estimator and then successively refines the estimator via multiple rounds of aggregations.The proposed estimator achieves the optimal convergence rate without any restriction on the number of blocks.We present both theoretical analysis and experiments to explore the property of the proposed method.
