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An Inconsistent Maximum Likelihood Estimate
Thomas S. Ferguson
Journal of the American Statistical Association
Vol. 77, No. 380 (Dec., 1982), pp. 831-834
Stable URL: http://www.jstor.org/stable/2287314
Page Count: 4
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An example is given of a family of distributions on [-1, 1] with a continuous one-dimensional parameterization that joins the triangular distribution (when θ = 0) to the uniform (when θ = 1), for which the maximum likelihood estimates exist and converge strongly to θ = 1 as the sample size tends to infinity, whatever be the true value of the parameter. A modification that satisfies Cramer's conditions is also given.
Journal of the American Statistical Association © 1982 American Statistical Association