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Title: Inference on level sets in functional linear regression Authors:  Masaaki Imaizumi - The University of Tokyo (Japan) [presenting]
Abstract: An inference method on active domains of functional data is developed via a functional linear regression and a principal component analysis (PCA) based estimator. In a linear regression model with a functional covariate and a scalar response variable, an active domain of a functional covariate is defined as a subset of a domain on which a functional data has a positive effect on outputs. Based on a functional linear regression model, an active domain is regarded as a level set of a slope function of the regression model. We propose an estimator for an active set by combining the PCA-based estimator and a kernel convolution approach. Also, we provide a multiplier bootstrap method for confidence analysis for an active set based on the high-dimensional Gaussian approximation technique. Our confidence analysis is shown to be valid asymptotically with ordinal conditions for a PCA-based estimator. We also propose a practical selection method for hyperparameters such as a cut-off level for basis functions and kernel width. The experimental analysis supports the validity of our method.