Additive regression for predictors of various natures and possibly incomplete Hilbertian responses
| Autor: | Jeong Min Jeon, Ingrid Van Keilegom, Byeong U. Park |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Statistics::Theory Statistics & Probability Asymptotic distribution incomplete response 02 engineering and technology 01 natural sciences VARIABLES Statistics::Machine Learning 010104 statistics & probability smooth backfitting CONVERGENCE 0202 electrical engineering electronic engineering information engineering Statistics::Methodology Applied mathematics ALGORITHM 0101 mathematics Additive model Mathematics Science & Technology Nonparametric statistics Estimator 020206 networking & telecommunications Regression analysis ASYMPTOTIC PROPERTIES COMPOSITIONAL DATA Asymptotic theory (statistics) Regression mixed predictor TRANSFORMATION Physical Sciences Statistics Probability and Uncertainty Backfitting algorithm Hilbertian response |
| Zdroj: | Electronic Journal of Statistics |
| Popis: | In this paper we consider a fully nonparametric additive regression model for responses and predictors of various natures. This includes the case of Hilbertian and incomplete (like censored or missing) responses, and continuous, nominal discrete and ordinal discrete predictors. We propose a backfitting technique that estimates this additive model, and establish the existence of the estimator and the convergence of the associated backfitting algorithm under minimal conditions. We also develop a general asymptotic theory for the estimator such as the rates of convergence and asymptotic distribution. We verify the practical performance of the proposed estimator in a simulation study. We also apply the method to various real data sets, including those for a density-valued response regressed on a mixture of continuous and nominal discrete predictors, for a compositional response regressed on a mixture of continuous and ordinal discrete predictors, and for a censored scalar response regressed on a mixture of continuous and nominal discrete predictors. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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