Smoothing Spline Semiparametric Density Models (Joy Yu - UMass Amherst)

Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are flexible in incorporating domain knowledge and uncertainty regarding the shape of the density function. Existing literature on semiparametric density models is scattered and lacks a systematic framework. We consider a unified framework based on reproducing kernel Hilbert space for modeling, estimation, computation and theory. We propose a general (nonlinear) semiparametric density model which includes many existing models as special cases. In this talk, I will focus on the theoretic results for our proposed models. In particular, we establish joint consistency and derive convergence rates of the proposed estimators. In addition, we obtain the convergence rate of the parametric component in the standard Euclidean norm, as well as the convergence rate of the overall density function in the symmetrized Kullback-Leibler distance. Lastly, I will propose potential future work on nonparametric and semiparametric models with nonlinear structure for which our techniques could be modified and applied.