Abstract
Let X1 be a random variable with density function f(t), Ψ(t) be an increasing absolutely continuous function, Φ(t) be the inverse function to Ψ(t), and X2 be the random variable X2 = Φ(X1). We consider the maximum likelihood estimator for the density ψ of the function Ψ in the case when we observe two independent samples from the distributions of X1 and X2. Under appropriate conditions on the involved distributions, we prove the consistency of the maximum likelihood estimator. Bibliography: 1 title.
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References
W. H. Wong and X. Shen, “Probability inequalities for likelihood ratios and convergence rates of sieve MLEs,” Ann. Statist., 23, 339–362 (1995).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 160–165.
An erratum to this article is available at http://dx.doi.org/10.1007/s10958-007-0133-2.
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Solev, V.N., Haghighi, F. Estimation in a model with infinite-dimensional nuisance parameter. J Math Sci 137, 4567–4570 (2006). https://doi.org/10.1007/s10958-006-0252-1
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DOI: https://doi.org/10.1007/s10958-006-0252-1