Nonparametric Methods for Interpretable Copula Calibration and Sparse Functional Classification

Le résumé fourni par la source

Nonparametric estimation is a novelty statistical method which relaxes the distribution assumption about the relationship between response and covariate, in contrast to parametric estimation. This method has been applied in many field of interest, including density function, regression model and derivative function. One of the important application of nonparametric estimation is modelling dependence among random variables via copula approaches has attracted considerable research attention. With advances in data collection, the strength of dependence often varies according to some covariate, which motivates the dependence calibration using conditional copulas. We propose a penalized estimation framework for the copula parameter function that inherits the flexibility of a nonparametric method and, at the same time, yields a parsimonious and interpretable dependence structure. The theoretical analysis guarantees that the penalized estimators enjoy the oracle properties and behave asymptotically as well as their nonparametric counterparts, while numerical experiments demonstrate the improved empirical performance. We then apply the proposed method to a twin birth weights data. Another important application of nonparametric estimation is classifying the functional data. We consider the classification of sparse functional data that are often encountered in longitudinal studies and other scientific experiments. To utilize the information from not only the functional trajectories but also the observed class labels, we propose a probability enhanced method achieved by weighted support vector machine based on its Fisher consistency property to estimate the effective dimension reduction space. Since only a few measurements are available for some, even all, individuals, a cumulative slicing approach is suggested to borrow information across individuals. We provide justification for validity of the probability-based effective dimension reduction space, and a straightforward implementation that yields a low-dimensional projection space ready for applying standard classifiers. The empirical performance is illustrated through simulated and real examples, particularly in contrast to classication results based on the prominent functional principal component analysis.

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