Fan, Jian-qing, Peng, Liang, Yao, Qiwei and Zhang, Wenyang (2009) Approximating conditional density functions using dimension reduction. Acta mathematicae applicatae sinica (English series), 25 (3). pp. 445-456. ISSN 0168-9673
We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ τ X, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.
|Additional Information:||© 2009 Springer Science+Business Media|
|Uncontrolled Keywords:||conditional density function, dimension reduction, Kullback-Leibler discrepancy, local linear regression, nonparametric regression, Shannon’s entropy|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Statistics|
Actions (login required)
|Record administration - authorised staff only|