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EMILIO SEIJO, Columbia University

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Inference in some nonstandard problems
16 February 2012 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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We will start by considering some nonparametric regression models from the point of view of shape-restricted statistical inference. The first problem to be tackled will be that of multivariate convex regression. We will define the (nonparametric) least squares estimator of a multivariate convex regression function, describe its finite-sample properties and state its asymptotic consistency theorem. The behavior of the estimator under model uncertainty will also be discussed. In addition, we will show how similar techniques can be applied to regression models combining convexity with component-wise monotonicity restrictions. We will then state some open problems and ongoing research projects in this area.

In the second part of the talk we will be concerned with applications of the bootstrap to semiparametric models. We will focus on two cases: change-point regression and Manskiā€™s maximum score estimator. We will exhibit the inconsistency of the classical bootstrap in these scenarios and provide model-based bootstrap procedures that produce asymptotically valid confidence intervals. We will finish with a discussion of some open questions.

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