Nonparametric Methods for Incomplete Sample Clauses

Nonparametric Methods for Incomplete. Big Data Troyanskaya et al. (2001) propose a k-nearest neighbor single-imputation method (KN- Nimpute) and utilize subjects in the neighborhood to impute missing values, by a weighted average of observed values. The selection of neighbors is based on the Euclidean distance. Liao et al. (2014) extend the KNNimpute to account for the information contained in the nearest variables. Specifically, they proposed four variations of KNNimpute among which, two approaches are shown to outperform a standard MI method in the simulation study. However, an inevitable problem of incorporating standard k-nearest neighbor into imputation methods is the specification of k as their performance highly depends on x. Xxxx and Ramzan (2015) propose a new method that can automatically select the relevant neighbors, instead of depending on k. Such a method based on a distance which uses the correlation among variables preforms well, especially when there are a large number of variables. Random forest, an ensemble method for classification and regression tasks, is widely used by researchers to cope with big data. As a nonparametric method, it allows com- plex interactive and non-linear relations between variables of different types. Stekhoven and Bu¨hlmann (2012) propose a random-forest-based imputation method (missForest) in which, for each variable with missing values, a random forest model is fitted using the observed values of that variable as the response and the remaining variables as predictors. By inheriting the power of random forest, missForest exhibits attractive computational efficiency and performs particularly well, compared with other parametric methods in the presence of mixed-type big data. Although the author argued that missForest intrinsically constitutes multiple imputation since many unpruned decision trees are averaged in the random forest procedure, it is not a proper imputation by the definition of Xxxxx (1987). This is because missForest predicts each missing value using a exact value rather than the random draw from a distribution. In a more recent paper, Shah et al. (2014) investigate the improper issue of missForest and proposed a new method (MICE-RF) within the mul- tiple imputation by chained equation framework, where multiple bootstrap samples of the original data are used to generate multiple imputed data sets. The step of bootstrapping accommodates the sampling variation and thus ensures proper imputations. Xxxxxxxxxx and Van Aelst (2015) compare s...