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- Florian Leitenstorfer, Gerhard Tutz
- Biostatistics
- 2007

In many studies, it is known that one or more of the covariates have a monotonic effect on the response variable. In these circumstances, standard fitting methods for generalized additive models (GAMs) generate implausible results. A fitting procedure is proposed that incorporates monotonicity assumptions on one or more smooth components within a GAM… (More)

Common approaches to monotonic regression focus on the case of a unidimensional covariate and continuous dependent variable. Here a general approach is proposed that allows for additive and multiplicative structures where one or more variables have monotone influence on the dependent variable. In addition the approach allows for dependent variables from an… (More)

- Florian Leitenstorfer, Gerhard Tutz
- Computational Statistics & Data Analysis
- 2007

A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g.… (More)

- Gerhard Tutz, Florian Leitenstorfer
- Computational Statistics & Data Analysis
- 2006

A shrinkage type estimator is introduced which has favourable properties in binary regression. The proposed response shrinkage estimator is based on a smoothedversion of the observed responseswhich is obtained by shifting the observation slightly towards the mean of the observations and therefore closer to the underlying probability. Estimates of this type… (More)

In single-index models the link or response function is not considered as fixed. The data determine the form of the unknown link function. In order to obtain a flexible form of the link function we specify the link function as an expansion in basis function and propose to estimate parameters as well as the link function by weak learners within a boosting… (More)

In many applications it is known that the underlying smooth function is constrained to have a specific form. In the present paper, we propose an estimation method based on the regression spline approach, which allows to include concavity or convexity constraints in an appealing way. Instead of using linear or quadratic programming routines, we handle the… (More)

- Florian Leitenstorfer, Gerhard Tutz
- GfKl
- 2006

In many studies where it is known that one or more of the certain covariates have monotonic effect on the response variable, common fitting methods for generalized additive models (GAM) may be affected by a sparse design and often generate implausible results. A fitting procedure is proposed that incorporates the monotonicity assumptions on one or more… (More)

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