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Local polynomial regression for pooled response data. (English) Zbl 1466.62302

This paper is a study on local polynomial estimators for the mean of a continuous response given covariates using pooled response data and individual-level covariate data. The authors proposed three local polynomial estimators for the mean function based on data, where they assume that data arise from random pooling. They present local polynomial estimators based on homogeneous pooled data and asymptotic properties of these estimators are investigated and compared in under each of the two pooling designs. They describe bandwidth selection methods tailored for the proposed estimators. They investigated asymptotic properties of these estimators and compared under each of the two pooling designs. Some simulations are carried out to compare different estimators for the mean function. They conducted analyse data from two real-life applications to illustrate the proposed local linear estimators for a conditional mean function. Finally, the authors present which estimators are best in each of the different possible situations.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
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