Confidence Intervals for Nonparametric Regression Functions with Missing Data

Yongsong Qin, Tao Qiu and Qingzhu Lei

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 19, 4123-4142

Abstract: Suppose that we have a nonparametric regression model Y = m(X) + ε with X ∈ Rp, where X is a random design variable and is observed completely, and Y is the response variable and some Y-values are missing at random. Based on the “complete” data sets for Y after nonaprametric regression imputation and inverse probability weighted imputation, two estimators of the regression function m(x0) for fixed x0 ∈ Rp are proposed. Asymptotic normality of two estimators is established, which is used to construct normal approximation-based confidence intervals for m(x0). We also construct an empirical likelihood (EL) statistic for m(x0) with limiting distribution of χ21, which is used to construct an EL confidence interval for m(x0).

Date: 2014
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DOI: 10.1080/03610926.2012.705210

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