Random forests, nonparametric and screening methods

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Data are increasing both in quantity and complexity and new statistical methods that can handle more and more complex situations are required. The research program of this proposal is divided into three parts: 1) Random forests for complex problems, 2) Nonparametric inference for multivariate data, 3) High-dimensional variable screening.****Random forests are among the most popular, accurate and versatile prediction and modeling methods. One big advantage of random forests is that they can automatically detect interactions without the need to specify a parametric form. They are even more pertinent nowadays, in the big data era, since they are well adapted for parallel computations. The first part of this research program proposes to extend random forests to complex problems, like the modeling of survival data with censoring, and the treatment of longitudinal data where the observations are dependent.****The validity of classical inference methods rely on certain distributional assumptions and many are non-robust when they are not verified. The second part of this research program will propose nonparametric methods for various problems with multivariate responses, like clustered data, mixed types of responses, and one-sided alternatives. Methods for global novelty detection will also be developed. ****The screening of variables in ultrahigh dimension aims at quickly reducing the dimensionality so other variable selection methods can be applied. The third part of this research program will develop fast robust screening methods with a data-driven way to select the number of variables to retain, in different modeling situations. ***One major impact of the research in this proposal is for the users of the methods since we will disseminate computer code for the methods developed in this research program. ********