Title: Nonparametric estimation of a latent variable model - a new approach
Authors: Augustin Kelava - Eberhard Karls Universitaet Tuebingen (Germany)
Michael Kohler - Technische Universitaet Darmstadt (Germany)
Adam Krzyzak - Concordia University (Canada)
Tim Fabian Schaffland - University of Tuebingen (Germany) [presenting]
Abstract: A new nonparametric latent variable approach is presented. The model is estimated without specifying the underlying distributions of the latent variables. In a first step, we fit a common factor analysis model to the observed variables. The main trick in estimation of the common factor analysis model is to estimate the values of the latent variables in such a way that the corresponding empirical distribution asymptotically satisfies the conditions that characterize the distribution of the latent variables uniquely. In a second step, we apply suitable nonparametric regression techniques to analyze the relation between the latent variables in this model. Theoretical results (e.g., concerning consistency of the estimates) are briefly presented. Furthermore, the finite sample size performance of the proposed approach is illustrated by applying it to simulated data in simulation studies.