Pei Geng

Michigan State University
, BH 227

Abstract

Model Checking in Tobit Errors-in-Variables Regressionusing Validation Data

Many countries conduct national surveys to col-lect information on the income of a household and their basicexpenditures such as automobile expenses. Studies in the pasthave shown that income data from such surveys is largely un-derreported. Additionally, for those households that do not ownvehicles, their expenditure data is censored at zero. To study therelationship between automobile expenditure and income, Tobitregression introduced by Tobin (1958) is used to model the non-negative response variable (automobile expenditure) while theerrors-in-variables model is adapted to model the independentvariable (income) with the use of validation data. We propose anonparametric test procedure utilizing kernel regression estima-tors and U statistic to verify the underlying regression function.We further derive the asymptotic normality under the null andalternative hypotheses. Simulation studies indicate robustnessand higher power of the test when compared to other leadingmethods. A real data application of the proposed method pro-vides consistent results and validates the current understandingof the dataset.