Robust estimation of single index models with responses missing at random

Ash Abebe (), Huybrechts F. Bindele (), Masego Otlaadisa () and Boikanyo Makubate ()
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Ash Abebe: Auburn University
Huybrechts F. Bindele: University of South Alabama
Masego Otlaadisa: Botswana International University of Science and Technology (BIUST)
Boikanyo Makubate: Botswana International University of Science and Technology (BIUST)

Statistical Papers, 2021, vol. 62, issue 5, No 7, 2195-2225

Abstract: Abstract A single-index regression model is considered, where some responses in the model are assumed to be missing at random. Local linear rank-based estimators of the single-index direction and the unknown link function are proposed. Asymptotic properties of the estimators are established under mild regularity conditions. Monte Carlo simulation experiments show that the proposed estimators are more efficient than their least squares counterparts especially when the data are derived from contaminated or heavy-tailed model error distributions. When the errors follow a normal distribution, the least squares index direction estimator tends to be more efficient than the rank-based index direction estimator; however, the least squares link function estimator remains less efficient than the rank-based link function estimator. A real data example is analyzed and cross-validation studies show that the proposed procedure provides better prediction than the least squares method when the responses contain outliers and are missing at random.

Keywords: Wilcoxon estimator; Consistency; Asymptotic normality; Missing at random; Imputation; Primary 62J02; 62G05; Secondary 62F12; 62G20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01184-2

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