Statistics Seminar（2015-10）

Topic：Sieve Estimation of Pairwise Comparison Models

Speaker：Jong-Myun Moon, University of College London

Time：Tuesday, 16^thJune, 14:00-15:30

Location：K01 of Guanghua Hotel

Abstract：We consider a situation when parameters of interest can be identified, without identifying nuisance parameters, by a certain comparison of two independent samples. When nuisance parameters are difficult to estimate, such an identification strategy is particularly attractive. A natural estimator is then obtained by minimizing a sum of all pairwise comparisons, which is a U-process of degree 2. When the estimated parameter is Euclidean, the asymptotic property of such an estimator is completely solved by Sherman (1993,1994). Our contributions are as follows. First, an infinite-dimensional (function) parameter along with the Euclidean parameter is included in the estimation. We employ the method of sieves and estimate both parameters jointly. In particular, a so-called single-index or bundled-parameter structure is allowed in the sieve estimation. Second, we propose a pairwise weighted bootstrap and prove its asymptotic validity. The literature lacks a simulation-based inference procedure even for the Euclidean parameter case. Lastly, we apply the developed asymptotic theory to non-parametric transformation models and the clustering analysis. Both estimators are new and can be of independent interest.

Your participation is warmly welcomed!