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We examine the integrated squared difference, also known as the L2 distance(L2D), between two probability densities. Such a distance metric allows forcomparison of differences between pairs of distributions or changes in adistribution over time. We propose a targeted maximum likelihood estimator forthis parameter based on samples of independent and identically distributedobservations from both underlying distributions. We compare our method tokernel density estimation and demonstrate superior performance for our methodwith regards to confidence interval coverage rate and mean squared error.

Targeted Estimation of L2 Distance Between Densities and its Application to Geo-spatial Data