Truncation and Unidentifiability: The Single Sample Case

Sunil Sapra


The problem of unidentifiability of regression coefficients due to truncation has been studied by Hodoshima (1988), under the assumptions that the error term has a strongly unimodal density and that the supports of the probability density functions (pdf’s) under complete and truncated data do not depend on unknown parameters. This article studies unidentifiability of certain parameters of the complete data pdf due to truncation in the single sample case without the necessity of assuming a strongly unimodal density. It is shown that if the complete data pdf can be written in a special multiplicative form, then the unknown parameter on which the support of the pdf depends, is not identified from the truncated density. Since the results of this paper hold in the single sample case under less restrictive assumptions than Hodoshima’s, an implication of our results is that unidentifiability due to truncation is somewhat more common in the single sample case than in the regression context. Some examples of pdf’s for which unidentifiability can occur due to truncation are also given.


Unidentifiability; Complete data; Truncated data

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