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ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used to model the main eeects, and their tensor products are used to(More)
A method of estimating an unknown density function f based on sample data is studied. Our approach is to use maximum likelihood etimation to estimate log(f) by a function s from a space of cubic splines that have a finite number of prespecified knots and are linear in the tails. The knots are placed at selected order statistics of the sample data. The(More)
The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional(More)
An automatic procedure that uses linear splines and their tensor products is proposed for tting a regression model to data involving a polychotomous response variable and one or more predictors The tted model can be used for multiple classi cation The automatic tting procedure involves maximum likelihood estimation stepwise addition stepwise deletion and(More)
The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log-likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots(More)