A proof of the ineffectiveness of likelihood inference on singular measures |
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Authors: | Mauro Piccioni |
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Institution: | Istituto di Matematica, Informatica e Sistemistica dell''Università di Udine, Via Mantica 3, 33100 Udine, Italy |
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Abstract: | This paper is devoted to showing that likelihood inference on a statistical model which consists of mutually singular probability measures may be ineffective when the supports of those measures intersect. The problem is examined in an abstract metric setting appropriate for statistical inference about stochastic procesess. An important example is discussed: the estimation of the (constant) diffusion term of a stochastic differential equation. |
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Keywords: | likelihood ratio singular measures |
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