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Simultaneous confidence intervals for semiparametric logistics regression and confidence regions for the multi-dimensional effective dose. (English) Zbl 1187.62090

Summary: We construct pointwise and simultaneous confidence intervals for the link function in a semiparametric logistic regression model based on the logit link function. Simultaneous confidence intervals are especially important for semiparametirc regression models since they allow inference to be made over the whole predictor space. These intervals are used to construct confidence regions for the multi-dimensional effective dose, that is for the set of multivariate covariate values where the probability that the binary response is one is equal to a preassigned value \(p\). We construct methods using inequalities, asymptotics and a semiparametric bootstrap. Simulations and examples are provided to demonstrate the performance and to compare the methods. The bootstrap procedure yields accurate confidence regions for the multi-dimensional effective dose.

MSC:

62G15 Nonparametric tolerance and confidence regions
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62J12 Generalized linear models (logistic models)
62G09 Nonparametric statistical resampling methods
65C60 Computational problems in statistics (MSC2010)
62P10 Applications of statistics to biology and medical sciences; meta analysis
62H12 Estimation in multivariate analysis
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