Far East Journal of Theoretical Statistics
Volume 27, Issue 2, Pages 193 - 218
(March 2009)
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MARGINAL DISTRIBUTIONS OF MAXIMUM LIKELIHOOD ESTIMATOR WHEN ONE OR TWO COMPONENTS OF THE TRUE PARAMETER ARE ON THE BOUNDARY OF THE PARAMETER SPACE
Marco Barnabani (Italy)
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Abstract: When the true parameter lies on the boundary of the parameter space, it is difficult to investigate the asymptotic distribution of maximum likelihood estimator. In some relatively simple cases, it is a mixture of truncated normal distributions. In this paper, we shall be concerned with the marginal distributions of maximum likelihood estimator when one or two components of the true parameter are zero and can be on the boundary of the parameter space. We have found that these distributions are (mixtures of) normal or truncated normal multiplied by “skew functions” which distort the symmetry of the normality. Some of these are skew-normal. |
Keywords and phrases: non-regular problem, marginal density function, truncated multivariate normal, skew function, skew-normal. |
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