Testing goodness of fit via nonparametric function estimation techniques

An overview is given of methodology for testing goodness of fit of parametric models using nonparametric function estimation techniques. The ideas are illustrated in two settings: the classical one-sample goodness-of-fit scenario and testing the goodness of fit of a polynomial regression model.     

Location and scale parameter estimation from randomly censored data

The problem of location and scale parameter estimation from randomly censored data is analyzed through use of a regression model for the Kaplan-Meier quantlle process. Continuous time regression techniques are employed to construct estimators that are both asymptotically normal and efficient. Estimators with a particularly simple form are obtained for the Koziol-Green model for random censorship. In the event of no censoring the regression model, and resulting estimators, reduce to those proposed by Parzen (1979 a, b).     

A family of minimum quantile distance estimators for the three-parameter Weibull distribution

A family of minimum quantile distance estimators, based on a subset of the sample quantiles, is proposed for the parameters of the three-parameter Weibull distribution. The estimation procedure is applicable to either complete or censored samples and, through use of the associated distance measure, provides a goodness-of-fit test for the Weibull model. The proposed estimators are both consistent and asymptotically normal and, in a particular instance, are optimal over the class of all estimators based on the same quantile subset. The problem of optimal quantile selection is also considered.     

Convergence rates for smoothing spline estimators in varying coefficient models

We consider the estimation of a multiple regression model in which the coefficients change slowly in “time”, with “time” being an additional covariate. Under reasonable smoothness conditions, we prove the usual expected mean square error bounds for the smoothing spline estimators of the coefficient functions.