Structure selection for bounded-parameter models: consistency conditions and selection criterion

Strong-consistency conditions for structure selection in bounded-parameter models are studied. A certain robust selection criterion, based on the volume of the exact parameter-bounding polytope, is proposed for linear regression models. The effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters. Its strong consistency is proved for a large class of noise distributions. The usual assumptions on the noise, namely independence, constant variance, or martingale difference properties, need not be made, but asymptotic independence is assumed