A comparison study of nonparametric imputation methods

Abstract

Consider estimation of a population mean of a response variable when the observations are missing at random with respect to the covariate. Two common approaches to imputing the missing values are the nonparametric regression weighting method and the Horvitz-Thompson (HT) inverse weighting approach. The regression approach includes the kernel regression imputation and the nearest neighbor imputation. The HT approach, employing inverse kernelestimated weights, includes the basic estimator, the ratio estimator and the estimator using inverse kernel-weighted residuals. Asymptotic normality of the nearest neighbor imputation estimators is derived and compared to kernel regression imputation estimator under standard regularity conditions of the regression function and the missing pattern function. A comprehensive simulation study shows that the basic HT estimator is most sensitive to discontinuity in the missing data patterns, and the nearest neighbors estimators can be insensitive to missing data patterns unbalanced with respect to the distribution of the covariate. Empirical studies show that the nearest neighbor imputation method is most effective among these imputation methods for estimating a finite population mean and for classifying the species of the iris flower data.

Nearest-Neighbor Estimation for ROC Analysis under Verification Bias

“…Hence, conditions stated in the theorem allow to apply the arguments given in the proof of Theorem 1 in Ning and Cheng [9] showing, in particular, that…”

“…Proof 1 Since EðD 2 Þ < 1; VarðDjY ¼ yÞ ¼ ρðyÞð1 À ρðyÞÞ < 1; ρðyÞ and πðyÞ are finite and first order differentiable, by Theorem 1 in Ning and Cheng [9], the KNN imputation estimatorθ 1 is consistent and asymptotically normally distributed, that is…”

“…To avoid misspecification problems, in what follows we propose a fully nonparametric approach to the estimation of SeðcÞ and SpðcÞ: Our approach is based on the K-nearest-neighbor (KNN) imputation estimator of the mean of a response variable as discussed in Ning and Cheng [9].…”

“…Let θ 1 be the disease prevalence, i.e., θ 1 ¼ EðDÞ ¼ PrðD ¼ 1Þ: As θ 1 is a mean, following Ning and Cheng [9], for a finite positive integer K and a suitable distance measure, a nearest-neighbor imputation estimator of θ 1 , based on the sample ðY i ; D i ; V i Þ; i ¼ 1; . .…”

“…The proposed method is based on nearest-neighbor imputation and adopts generic smooth regression models for both the probability that a subject is diseased and the probability that it is verified. Our choice is motivated by the results in Ning and Cheng [9], according to which the nearest-neighbor imputation method favorably compares with other nonparametric imputation methods in estimating a population mean.…”