Statistical estimation for truncated exponential families
The exponential family of distributions with one natural parameter truncated either from one or both sides is considered. Two situations are studied. First, the natural parameter is a parameter of interest while a truncation parameter is considered to be a nuisance parameter. Second, the truncation parameter is a parameter of interest and the natural parameter is a nuisance parameter. The parameter of interest is estimated by a maximum likelihood estimate supposing the nuisance parameter is known and by a bias adjusted maximum likelihood estimate supposing the nuisance parameter is unknown. Moreover, in the case of the natural parameter being the parameter of interest a maximum conditional likelihood estimator is also considered. The second-order asymptotical variances of these estimates obtained from the stochastic expansions are compared. The results are illustrated by several examples, i.e. by a truncated exponential, a truncated normal, an upper-truncated Pareto, a truncated beta and truncated Erlang distributions.
scientific article; zbMATH DE number 6802167