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Abstract:
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With the prevalence of more complex data, statisticians face the task of developing appropriate regression models when the responses lie in a metric space while the predictors lie in Rp. To tackle this, the global Fréchet model was developed as a generalization of linear regression and can handle predictors of any fixed dimension. The local Fréchet model, as a generalization of local linear regression, allows for more flexible regression relationships but has only been developed for a single predictor. In this talk, this methodology will be expanded to allow for flexible model fits when p>1 predictors are present by developing the Fréchet Single Index(FSI) model. An intuitive procedure for estimating both the index and the Fréchet regression function are outlined using a combination of local Fréchet regression and univariate M-estimation. Simulations with response objects lying on the surface of a unit sphere demonstrate consistency of model estimation. Additionally, analysis of a human mortality data set illustrates how the FSI model can be used to investigate how various socioeconomic factors affect age-of-death distributions which are viewed as elements of Wasserstein space.
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