In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are hea...In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are heavy-tailed and may not even possess variances or means.The main contribution of this paper is that we establish some oracle inequalities for the inverse problems by using quantile coupling technique that gives a tight bound for the quantile coupling between an arbitrary sample p-quantile and a normal variable,and an automatic selection principle for the nonrandom filters.This leads to the data-driven choice of weights.We also give an algorithm for its implementation.The quantile coupling inequality developed in this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.展开更多
An adaptive local smoothing method for nonparametric conditional quantile regression models is considered in this paper. Theoretical properties of the procedure are examined. The proposed method is fully adaptive in t...An adaptive local smoothing method for nonparametric conditional quantile regression models is considered in this paper. Theoretical properties of the procedure are examined. The proposed method is fully adaptive in the sense that no prior information about the structure of the model is assumed. The fully adaptive feature not only allows varying bandwidths to accommodate jumps or instantaneous slope changes, but also allows the algorithm to be spatially adaptive. Under general conditions, precise risk bounds for homogeneous and heterogeneous cases of the underlying conditional quantile curves are established. An automatic selection algorithm for locally adaptive bandwidths is also given, which is applicable to higher dimensional cases. Simulation studies and data analysis confirm that the proposed methodology works well.展开更多
When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of ...When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.展开更多
基金supported by the Major Project of Humanities Social Science Foundation of Ministry of Education(Grant No. 08JJD910247)Key Project of Chinese Ministry of Education (Grant No. 108120)+4 种基金National Natural Science Foundation of China (Grant No. 10871201)Beijing Natural Science Foundation (Grant No. 1102021)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No. 10XNL018)the China Statistical Research Project (Grant No. 2011LZ031)
文摘In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are heavy-tailed and may not even possess variances or means.The main contribution of this paper is that we establish some oracle inequalities for the inverse problems by using quantile coupling technique that gives a tight bound for the quantile coupling between an arbitrary sample p-quantile and a normal variable,and an automatic selection principle for the nonrandom filters.This leads to the data-driven choice of weights.We also give an algorithm for its implementation.The quantile coupling inequality developed in this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.
基金supported by the major research projects of Philosophy and Social Science of the Chinese Ministry of Education(Grant No.15JZD015)National Natural Science Foundation of China(Grant No.11271368)+9 种基金the major program of Beijing Philosophy and Social Science Foundation of China(Grant No.15ZDA17)project of Ministry of Education supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130004110007)the Key Program of National Philosophy and Social Science Foundation Grant(Grant No.13AZD064)the major project of Humanities Social Science Foundation of Ministry of Education(Grant No.15JJD910001)Renmin University of China,the Special Developing and Guiding Fund for Building World-Class Universities(Disciplines)(Grant No.15XNL008)China Statistical Research Project(Grant No.2016LD03)the Fund of the Key Research Center of Humanities and Social Sciences in the general Colleges and Universities of Xinjiang Uygur Autonomous RegionGeneral Research Fund of Hong Kong Special Administrative Region Research Grants Council General Research Fund(Grant Nos.14300514 and 14325612)Hong Kong Special Administrative Region-Research Grants Council Collaborative Research Fund(Grant No.City U8/CRG/12G)the Theme-Based Research Scheme of Hong Kong Special Administrative Region-Research Grants Council Theme Based Scheme(Grant No.T32-101/15-R)
文摘An adaptive local smoothing method for nonparametric conditional quantile regression models is considered in this paper. Theoretical properties of the procedure are examined. The proposed method is fully adaptive in the sense that no prior information about the structure of the model is assumed. The fully adaptive feature not only allows varying bandwidths to accommodate jumps or instantaneous slope changes, but also allows the algorithm to be spatially adaptive. Under general conditions, precise risk bounds for homogeneous and heterogeneous cases of the underlying conditional quantile curves are established. An automatic selection algorithm for locally adaptive bandwidths is also given, which is applicable to higher dimensional cases. Simulation studies and data analysis confirm that the proposed methodology works well.
基金supported by the National Natural Science Foundation of China under Grant No.11271368the Major Program of Beijing Philosophy and Social Science Foundation of China under Grant No.15ZDA17+3 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20130004110007the Key Program of National Philosophy and Social Science Foundation under Grant No.13AZD064the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China under Grant No.15XNL008the Project of Flying Apsaras Scholar of Lanzhou University of Finance & Economics
文摘When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.
