Specification tests in nonparametric regression

Consider the location-scale regression model Y = m ( X ) + σ ( X ) ɛ , where the error ɛ is independent of the covariate X, and m and σ are smooth but unknown functions. We construct tests for the validity of this model and show that the asymptotic limits of the proposed test statistics are distribution free. We also investigate the finite sample properties of the tests through a simulation study, and we apply the tests in the analysis of data on food expenditures.