Numerical experience with modern estimation algorithms

Examples are presented that demonstrate various numerical phenomena associated with modern estimation. Many of the key numerical problems do not require high dimensionality or large numbers of arithmetic operations. Our goal is to alert estimation users and algorithm designers to the frailties still existent with modern computation. It is hoped that by showing how simple examples can "fall apart", one will be less tempted to relegate the use of sound numerical procedures to only the (known) difficult problems.