Li, Jialiang; Zhang, Chunming; Doksum, Kjell A.; Nordheim, Erik V. Simultaneous confidence intervals for semiparametric logistics regression and confidence regions for the multi-dimensional effective dose. (English) Zbl 1187.62090 Stat. Sin. 20, No. 2, 637-659 (2010). 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. Cited in 4 Documents 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 Keywords:bootstrap; local likelihood; multi-dimensional effective dose; semiparametric logistic regression model; simultaneous confidence interval; tables PDFBibTeX XMLCite \textit{J. Li} et al., Stat. Sin. 20, No. 2, 637--659 (2010; Zbl 1187.62090) Full Text: Link