Title: Inference when using nearest neighbors methods and the bootstrap
Authors: Shahla Faisal - Ludwig Maximilians University Munich (Germany) [presenting]
Christian Heumann - Ludwig-Maximilians-University Munich (Germany)
Gerhard Tutz - Ludwig-Maximilians-University Munich (Germany)
Abstract: Imputation is an attractive approach for filling the missing data values with their estimates. A number of methods are available in literature that can be used for imputing the missing data. However it is not advisable to treat the imputed data just as the complete data. Applying the existing methods to analyse the imputed data, for example, to estimate the variance and/or statistical inference will probably produce invalid results because these methods do not account for the uncertainty of imputations. We present analytic techniques for inference from a dataset in which missing values have been replaced by nearest neighbors imputation method. A simple and easy to use bootstrap algorithm that combines the nearest neighbors imputation with bootstrap resampling estimation to obtain valid bootstrap inference in a linear regression model is suggested. More specifically, imputing the bootstrap samples in the exact same way as original data was imputed produces correct bootstrap estimates. Simulation results show the performance of our approach in different data structures.