Parameter estimation from small biased samples: Fuzzy sets vs statistics

We consider a problem of estimating an unknown location parameter from several small biased samples. The biases and scale parameters of the samples are not known as well. For the case of two samples a fuzzy estimator based on a triangular membership function is introduced and studied. In particular, it is shown that its asymptotic bias is less than that of the weighted mean for the majority of key parameters in the problem. For small samples the fuzzy estimator is compared with the weighted mean and weighted median for a bunch of distributions. The main conclusion is that the fuzzy estimator performs better in most of the scenarii, however its advantage is subtle except for a few cases. Similar conclusions are obtained for the case of three information sources. The theoretical and simulation results for two samples might serve as a guidance for choosing a particular estimation method from the discussed ones based on preliminary information on relations between unknown parameters.