**SPEAKER:** Dr. Yehua Li

Dept. of Statistics, UGA

**ABSTRACT:**

In this paper, we consider regression models with a functional predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these projections is called the effective dimension reduction (EDR) space. To determine the dimensionality of the EDR space, we focus on the principal component scores of the functional predictor, and propose two sequential chi-square testing procedures under the assumption that the predictor has an elliptically contoured distribution. We further extend these procedures and introduce an adaptive Neyman test that simultaneously takes into account a large number of principal component scores. These tests can be used for model building or as goodness-of-fit tests in the context of functional linear models and functional projection pursuit models. The proposed procedures are supported by theory, validated by simulation studies, and illustrated by a real-data example. Although our methods and theory were developed under the functional data framework, they are applicable to general high-dimensional data.

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