Bose and Lin introduced a class of systematic codes for detection of binary asymmetric errors. Later, in [4] this class was generalized and the Generalized Bose-Lin (GBL) codes were introduced. In this note, we describe a Generalized Bose-Lin codes of limited magnitude l. For these codes, the possible undetectable errors are characterized, the undetectable errors of minimum weight are determine...

Common approximations for the minimum description length (MDL) criterion imply that the cost of adding a parameter to a model fit to n observations is about (1/2) log n bits. While effective for parameters which are large on a standardized scale, this approximation overstates the parameter cost near zero. A uniform approximation and local asymptotic argument show that the addition of a small pa...

The behavior of a minimizing point when an objective function is tilted by adding a small linear term is studied from the perspective of second-order conditions for local optimality. The classical condition of a positive-definite Hessian in smooth problems without constraints is found to have an exact counterpart much more broadly in the positivity of a certain generalized Hessian mapping. This...