The technique of using densities and conditional distributions to carry out consistent specification testing and model selection amongst multiple diffusion processes have received considerable attention from both financial theoreticians and empirical econometricians over the last two decades....

This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any functions, including ones carrying an index, which can be...