Abstract
We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The consistency and super-efficiency of this maximum leave-one-out likelihood estimator is shown through a direct argument. The importance for estimation within parametric families is discussed and illustrated by an example involving the gamma mixture of normal distributions.
Original language | English |
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Pages (from-to) | 19-38 |
Journal | Annals of the Institute of Statistical Mathematics |
Volume | 67 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2015 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- Unbounded likelihood
- Location parameter
- Super-efficiency
- Generalized
- asymmetric Laplace distribution