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We study an estimator for smoothing irregularly sampled data into a smoothmap. The estimator has been widely used in astronomy, owing to its low level ofnoise; it involves a weight function -- or smoothing kernel -- w(\theta). Weshow that this estimator is not unbiased, in the sense that the expectationvalue of the smoothed map is not the underlying process convolved with $w$, buta convolution with a modified kernel w_eff(\theta). We show how to calculatew_eff for a given kernel w and investigate its properties. In particular, it isfound that (1) w_eff is normalized, (2) has a shape `similar' to the originalkernel w, (3) converges to w in the limit of high number density of datapoints, and (4) reduces to a top-hat filter in the limit of very small numberdensity of data points. Hence, although the estimator is biased, the bias iswell understood analytically, and since w_eff has all the desired properties ofa smoothing kernel, the estimator is in fact very useful. We present explicitexamples for several filter functions which are commonly used, and provide aseries expression valid in the limit of large density of data points.Comment: 11 pages, submitted to A&

Smooth maps from clumpy data