Abstract
This chapter discusses asymptotically complete classes. If for arbitrarily large sample sizes tests of uniform deficiency 0 exist, then the family is necessarily exponential. Besides the exponential families, for which tests of uniform deficiency 0 exist, there are other families admitting tests whose asymptotic deficiency is 0 for all β∈(0,1). If an explicit formula for the maximum likelihood (m.l.) estimator is not available, it can be easier to use an initial estimator together with the more complex formula for B(n) than to use the simpler formula based on the m.l. estimator and to compute the m.l. estimate numerically. The chapter discusses the shape of the power functions by using graphical representation.
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