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Reducing the variance by smoothing |
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| Affiliation: | 1. Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia;2. Novosibirsk State University, Novosibirsk, 630090, Russia;1. Department of Chemical Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran;2. Department of Chemistry, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran;3. Faculty of Chemical Engineering, Babol University of Technology, Babol, Iran |
| Abstract: | In this paper we show that versions of statistical functionals which are obtained by smoothing the corresponding empirical d.f. with an appropriate kernel can reduce the variance and the mean square error of the statistic. This is shown by studying the influence function of the functional. The smaller variance is achieved when the influence function is either discontinuous or piecewise linear with convexity towards the x-axis. Examples for M- and L-estimators are given. |
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