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Title: Nonparametric estimation for big-but-biased data Authors:  Laura Borrajo - UDC (Spain) [presenting]
Ricardo Cao - University of Coruna (Spain)
Abstract: Nonparametric estimation for large-sized samples subject to sampling bias is studied. The general parameter considered is the mean of a transformation of the random variable of interest. When ignoring the biasing weight function, a small-sized simple random sample of the real population is assumed to be additionally observed. A new nonparametric estimator that incorporates kernel density estimation is proposed. Asymptotic properties for this estimator are obtained under suitable limit conditions on the two sample sizes and standard and non-standard asymptotic conditions on the two bandwidths. Explicit formulas are shown for the particular case of mean estimation. Simulation results show that the new mean estimator outperforms two classical ones. The influence of two smoothing parameters on the performance of the final estimator is also studied, exhibiting a striking behavior. The new method is applied to a real data set concerning airline on-time performance of US flights.