Parametric Conditional Mean and Variance Testing with Censored Data

Suppose the random vector (X, Y) satisfies the heteroscedastic regression model Y = m(X) + σ(X)ε, where m(·) = E(Y∣·), σ²(·) = Var(Y∣·) and ε (with mean zero and variance one) is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. New goodness-of-fit testing procedures for m and σ²(·) are proposed. They are based on a modified integrated regression function technique which uses the method of [Heuchenne and Van Keilegom, 2006b] to construct new versions of functions of the data points. Asymptotic representations of the processes are obtained and weak convergence to gaussian processes is deduced.