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清華大學統計學研究所
國立清華大學統計學研究所
2016-10-14(五),主講人:江金倉 教授 (台灣大學 應用數學科學研究所)

清華大學、交通大學

統 計 學 研 究 所

專 題 演 講

 


講 題: An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model   
演講者: 江金倉 教授 (台灣大學 應用數學科學研究所)
時 間: 105年10月14日(星期五)10:40 - 12:00  (上午10:20 - 10:40茶會於統計所821室舉行)
地 點: 綜合三館837室
摘 要: In the exploratory data analysis, the sufficient dimension reduction model has been widely used to characterize the conditional distribution of interest. Different from the existing approaches, our main achievement is to simultaneously estimate two essential elements, basis and structural dimension, of the central subspace and the bandwidth of a kernel distribution estimator through a single estimation criterion. With an appropriate order of kernel function, the proposed estimation procedure can be effectively carried out by starting with a dimension of zero until the first local minimum is reached. Meanwhile, the optimal bandwidth selector is ensured to be a valid tuning parameter for the central subspace estimator. An important advantage of this estimation technique is its flexibility to allow a response to be discrete and some of covariates to be discrete or categorical providing that a certain continuity condition holds. Under very mild assumptions, we further derive the uniform consistency of the introduced optimization function and the consistency of the resulting estimators. Moreover, the asymptotic normality of the central subspace estimator is established with an estimated rather than exact structural dimension. In extensive simulations, the developed approach generally outperforms the competitors. Data from previous studies are also used to illustrate the proposal. On the whole, our methodology is very effective in estimating the central subspace and conditional distribution, highly flexible in adapting diverse types of a response and covariates, and practically feasible in obtaining an asymptotically optimal and valid bandwidth estimator. (This is a joint work with Dr. Ming-Yueh Huang)

 

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