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The domain of existentially uncertain spatial data refers to objects that are modelled using an existential probability accompanying spatial data values. An interesting and challenging query type over existentially uncertain data is the search of the nearest neighbor (NN), since the probability of a potential dataset object to be the NN of the query object depends on the locations and probabilities of other points in the same dataset. In this paper, following a statistical approach, we estimate the average number of the NNsrequired to answer probabilistic thresholding NN(PTNN) queries as function of the threshold t, allowing us to utilize existing approaches and propose a cost model for such queries. Based on the same statistical approach, we propose an efficient algorithm for PTNN queries over arbitrarily structured existentially uncertain spatial data. Our experimental study demonstrates the accuracy and efficiency of the proposed techniques.