The estimation of the model order in exponential families

Estimators are sought that achieve high exponential rate of decrease in the underestimation probability while keeping the overestimation probability exponent at a certain prescribed level. It is assumed that a given integer is known to upper-bound the true order. Some examples are given of possible applications of the proposed method in specific order estimation and hypothesis testing problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>