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With the availability of more non-euclidean data objects, statisticians are faced with the task of developing appropriate statistical methods. For regression models in which the predictors lie in $R^p$ and the response variables are situated in a metric space, conditional Frechet means can be used to define the Frechet regression function. Global and local Frechet methods have recently been developed for modeling and estimating this regression function as extensions of multiple and local linear regression, respectively. This paper expands on these methodologies by proposing the Frechet Single Index (FSI) model and utilizing local Frechet along with $M$-estimation to estimate both the index and the underlying regression function. The method is illustrated by simulations for response objects on the surface of the unit sphere and through an analysis of human mortality data in which lifetable data are represented by distributions of age-of-death, viewed as elements of the Wasserstein space of distributions.
Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for regression models
We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for Roptimal designs, including scale invariance, reflection sym
Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations. Examples of such data objects include covariance matrices, graph Lap
Environmental variability often has substantial impacts on natural populations and communities through its effects on the performance of individuals. Because organisms responses to environmental conditions are often nonlinear (e.g., decreasing perfor
Field observations form the basis of many scientific studies, especially in ecological and social sciences. Despite efforts to conduct such surveys in a standardized way, observations can be prone to systematic measurement errors. The removal of syst