Scale checks in censored regression

Suppose the random vector (X,Y ) satisfies the regression model Y = m(X) + σ(X)ε, where m(·) and σ(·) are unknown location and scale functions and ε is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. A new test for a specific parametric form of any scale function σ(·) (including the standard deviation function) is proposed. Its statistic is based on the distribution of the residuals obtained from the assumed regression model. Weak convergence of the corresponding process is obtained and its finite sample behaviour is studied via simulations. Finally, characteristics of the test are illustrated in the analysis of a fatigue data set.