Abstract
Abstract Theil and Laitinen (1980) proposed a maximum entropy (ME) technique to estimate singular moment matrices arising from undersized samples. They fitted a continuous ME distribution to the values of a variable arranged in an ascending order of magnitude. In this paper we relax their continuity assumption and simplify matters from a practical viewpoint. Our continuity is restricted to a range around each observation arising from measurement errors. We propose measurement error maximum entropy (MEME or ME2) distribution yielding a positive definite estimate of the dispersion matrix for undersized samples. Some desirable properties of ME2 distribution are mentioned. An example illustrates the simplicity of our ME2 estimation and shows that our estimates can be closer to the true values.
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