Nonparametric imputation method for nonresponse in surveys

Many imputation methods are based on statistical models that assume that the variable of interest is a noisy observation of a function of the auxiliary variables or covariates. Misspecification of this model may lead to severe errors in estimates and to misleading conclusions. A new imputation method for item nonresponse in surveys is proposed based on a nonparametric estimation of the functional dependence between the variable of interest and the auxiliary variables. ∗Affiliation while the research was conducted: Institute of Statistics, University of Neuchâtel, Av. de Bellevaux 51, 2000 Neuchâtel, Switzerland. Current affiliation: Department of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, Ontario, M1C 1A4, Canada. †Department of Statistical Sciences, University of Toronto, 100 St. Georges Street, Toronto, Ontario, M5S 3G3, Canada 1 ar X iv :1 60 3. 05 06 8v 2 [ st at .M E ] 6 F eb 2 01 7 We consider the use of smoothing spline estimation within an additive model framework to flexibly build an imputation model in the case of multiple auxiliary variables. The performance of our method is assessed via numerical experiments involving simulated and real data.