ON IDENTIFIABILITY AND INFORMATION-REGULARITY IN PARAMETRIZED NORMAL-DISTRIBUTIONS

We describe methods to establish identifiability and information-regul arity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability dis tribution and they are information-regular when their Fisher informati on matrix is full rank. In normal distributions, information-regularit y implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without havin g to explicitly compute the information matrix. Some examples are give n.