Nonparametric Regression with Response Missing at Random and the Scale Depending on Auxiliary Covariates

• Activity Number: 492 - Application of Nonparametric Methods
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Tian Jiang* and Sam Efromovich
• Companies: The University of Texas At Dallas and University of Texas at Dallas
• Keywords: Adaptation; Availability likelihood; Curse of multidimensionality; Heteroscedasticity; MAR; Sharp minimaxity

Abstract

Nonparametric regression with missing at random (MAR) response, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that the heteroscedasticity and MAR affect the constant of the sharp minimax MISE convergence. The sharp minimax procedure is based on estimation of unknown nuisance scale function, design density and missing mechanism. The estimator is adaptive to the missing mechanism and unknown smoothness of the estimated regression function. The procedure is tested on simulated data and real examples, and the results justify practical feasibility of the proposed method for this complex regression setting.